JSFiddle - React, Tailwind, and code Playground

HTML

<div id="viewport">
    <ul id="list">
        <li class="above">Foo</li>
        <li class="selected">Bar</li>
        <li class="below">Barf</li>
        <li>Boo</li>
        <li>Huh</li>
        <li>Wha</li>
        <li>Oh</li>
    </ul>
</div>
<a href="#" id="up">UP</a> -- <a href="#" id="down">DOWN</a>

CSS

#viewport{
    height: 175px;
    overflow: hidden;
    padding: 0;
}

ul{
    list-style-type: none;
    padding: 0;
    margin: 0;
}

li{
    border: 1px solid #ccc;
    width: 70px;
    height: 50px;
    line-height: 50px;
    padding: 0 0 0 30px;
    margin: 5px;
    font-size: 1.5em;
    color: #999;
    background-color: #fed;
}

li.selected{
    border-radius: 20px;
    background-color: #fe0
}

li.above{
    border-radius: 10px;
    border-top-left-radius: 35px;    
}

li.below{
    border-radius: 10px;
    border-bottom-left-radius: 35px;    
}

JavaScript

var viewport = $('#viewport'),
    list = $('#list'),
    itemHeight = $('li', list).first().outerHeight(),
    btnUp = $('#up'),
    btnDown = $('#down'),
    busy = false,
    selected, above, below;

var update = function(){
    selected = $('li:nth-of-type(2)', list).addClass('selected', 200);
    above = selected.prev().addClass('above', 200);
    below = selected.next().addClass('below', 200); 
    setTimeout(function(){ busy = false; }, 200);
};

var goUp = function(){
    if(busy) return; else busy = true;
    $('li', list).removeClass('selected above below');
    list.animate({marginTop: -itemHeight}, 600, 'easeOutBounce', function(){ 
        list.css({marginTop: 0}).append($('li', list).first());
        update();
    });
}
var goDown = function(){
    if(busy) return; else busy = true;
    $('li', list).removeClass('selected above below');
    list
        .css({marginTop: -itemHeight})
        .prepend($('li',list).last())
        .animate({marginTop: 0}, 600, 'easeOutBounce', update);
}
btnUp.on('click', goUp);  
btnDown.on('click', goDown);