Edit in JSFiddle

bindClicks();
animate("down");

function animate(d) {
    
    // stacking order
    $('.content_container:first').css("z-index", "2");
    $('.content_container:last').css("z-index", "1");
    
    // animate fade and move background, only if count more than 1
    if ($(".content_container").length > 1) {
        if (d == "down") {
            $('.content_container:last').animate({ opacity: 0, top: "100%" }, 500, function() {});
        } else if (d == "up") {
            $('.content_container:last').animate({ opacity: 0, top: "-100%" }, 500, function() {});
        } else if (d == "left") {
            $('.content_container:last').animate({ opacity: 0, right: "100%" }, 500, function() {});
        } else if (d == "right") {
            $('.content_container:last').animate({ opacity: 0, right: "-100%" }, 500, function() {});
        }
    }
    
    // move top element in
    $('.content_container:first').animate({ top: "0%", right: "0%" }, 500, function() {
        // if there's more than one content_container, remove the last one
        if ($(".content_container").length > 1) {
            $('.content_container:last').remove();
            setTimeout(function () {
                $('.content_container').addClass("not_scaled"); 
            }, 750);
        }   
    });
    
} // end animate function   

function bindClicks() {
    $("a.button").click(function() {  
         $('.content_container').removeClass("not_scaled");
         a = $('.content_container').clone();
         a.addClass("scaled"); // start it scaled
        
         // set location of duplicated div off stage
         a.css("top", "0");
         a.css("right", "0");
         if ($(this).hasClass("down")) { a.css("top", "-100%"); }
         if ($(this).hasClass("up")) { a.css("top", "100%"); }
         if ($(this).hasClass("left")) { a.css("right", "-100%"); }
         if ($(this).hasClass("right")) { a.css("right", "100%"); }         
    
         $(".page_container").prepend(a);
         $('.content_container:last').addClass("scaled");
         
         var clickedItem = $(this);
         setTimeout(function (self) { 
             if (clickedItem.hasClass("down")) {
                 animate("down");
             } else if (clickedItem.hasClass("up")) {
                 animate("up");
             } else if (clickedItem.hasClass("left")) {
                 animate("left");
             } else if (clickedItem.hasClass("right")) {
                 animate("right");
             }
             bindClicks();
         }, 1000);
    }); // end a.button click
} // end bindClicks
<div class="page_container">
    <div class="content_container">
        <a class="button up" href="#">&uarr; Transition Up</a>
        <a class="button down" href="#">&darr; Transition Down</a>
        <a class="button left" href="#">&larr; Transition Left</a>
        <a class="button right" href="#">Transition Right &rarr;</a>
    </div>
</div>
body, html {
    height: 100%;
    width: 100%;
}
.page_container {
    background: url("http://www.dawsonmediadesign.com/images/thatch.jpg");        
    height: 100%;
    width: 100%;
}
.content_container {
    position: absolute;
    top: -100%;
    width:100%;
    min-height: 100%;
    background-color: white;
    margin: 0 auto;
    -webkit-box-shadow:0 0 10px #333; 
    -moz-box-shadow: 0 0 10px #333; 
    box-shadow:0 0 10px #333;
}
.scaled {
    transform: scale(0.95, 0.95); 
    -moz-transform: scale(0.95, 0.95); 
    -ms-transform: scale(0.95, 0.95); 
    -webkit-transform: scale(0.95, 0.95); 
    -o-transform: scale(0.95, 0.95);         
}
.not_scaled {
    transform: scale(1, 1); 
    -moz-transform: scale(1, 1); 
    -ms-transform: scale(1, 1); 
    -webkit-transform: scale(1, 1); 
    -o-transform: scale(1, 1); 
}
.scaled, .not-scaled {
    -webkit-transition: .5s ease-out;
    -moz-transition: .5s ease-out;
    -ms-transition: .5s ease-out;
    -webkit-transition: .5s ease-out;
    -o-transition: .5s ease-out;   
}

/* button code for illustration only */ 

.button {
    width: 140px;
    text-decoration: none;
    border:1px solid #25729a; 
    -webkit-border-radius: 3px; 
    -moz-border-radius: 3px;
    border-radius: 3px;
    font-family:arial, helvetica, sans-serif; 
    padding: 10px 10px 10px 10px; 
    text-shadow: -1px -1px 0 rgba(0,0,0,0.3);
    text-align: center; 
    color: #FFFFFF; 
    background-color: #3093c7;
    background-image: -webkit-gradient(linear, left top, left bottom, color-stop(0%, #3093c7), color-stop(100%, #1c5a85));
    background-image: -webkit-linear-gradient(top, #3093c7, #1c5a85);
    background-image: -moz-linear-gradient(top, #3093c7, #1c5a85);
    background-image: -ms-linear-gradient(top, #3093c7, #1c5a85);
    background-image: -o-linear-gradient(top, #3093c7, #1c5a85);
    background-image: linear-gradient(top, #3093c7, #1c5a85);filter:progid:DXImageTransform.Microsoft.gradient(GradientType=0,startColorstr=#3093c7, endColorstr=#1c5a85);
}

.button:hover{
    border:1px solid #1c5675;
    background-color: #26759e;
    background-image: -webkit-gradient(linear, left top, left bottom, color-stop(0%,#26759e), color-stop(100%, #133d5b));
    background-image: -webkit-linear-gradient(top, #26759e, #133d5b);
    background-image: -moz-linear-gradient(top, #26759e, #133d5b);
    background-image: -ms-linear-gradient(top, #26759e, #133d5b);
    background-image: -o-linear-gradient(top, #26759e, #133d5b);
    background-image: linear-gradient(top, #26759e, #133d5b);filter:progid:DXImageTransform.Microsoft.gradient(GradientType=0,startColorstr=#26759e, endColorstr=#133d5b);
}

.button.up {
    position: absolute;
    top: 20px;
    left: 50%; 
    margin-left: -70px;
}
.button.down {
    position: absolute;
    bottom: 20px;
    left: 50%; 
    margin-left: -70px;
}
.button.left {
    position: absolute;
    left: 20px;
    top: 50%; 
    margin-top: -15px;
}
.button.right {
    position: absolute;
    right: 20px;
    top: 50%; 
    margin-top: -15px;
}
.content_container {
    background: rgb(239,239,239); /* Old browsers */
background: -moz-radial-gradient(center, ellipse cover,  rgba(239,239,239,1) 0%, rgba(255,255,255,1) 100%); /* FF3.6+ */
background: -webkit-gradient(radial, center center, 0px, center center, 100%, color-stop(0%,rgba(239,239,239,1)), color-stop(100%,rgba(255,255,255,1))); /* Chrome,Safari4+ */
background: -webkit-radial-gradient(center, ellipse cover,  rgba(239,239,239,1) 0%,rgba(255,255,255,1) 100%); /* Chrome10+,Safari5.1+ */
background: -o-radial-gradient(center, ellipse cover,  rgba(239,239,239,1) 0%,rgba(255,255,255,1) 100%); /* Opera 12+ */
background: -ms-radial-gradient(center, ellipse cover,  rgba(239,239,239,1) 0%,rgba(255,255,255,1) 100%); /* IE10+ */
background: radial-gradient(ellipse at center,  rgba(239,239,239,1) 0%,rgba(255,255,255,1) 100%); /* W3C */
filter: progid:DXImageTransform.Microsoft.gradient( startColorstr='#efefef', endColorstr='#ffffff',GradientType=1 ); /* IE6-9 fallback on horizontal gradient */



    
}