Edit in JSFiddle

<a>Без перехода</a>
<a class="with-background-transition">Переход только для background</a>
<a class="with-all-transition">Переход для всех свойств</a>

a {
  background: lightgrey;
  color: grey;
  margin-right: 10px;
  padding: 5px 10px;
  transition: none;
  cursor: pointer;
  text-decoration: underline;
}

a:hover {
  background: yellow;
  border: 5px solid blue;
  color: green;
}

a.with-background-transition {
  transition-duration: 2s;
  transition-property: background;
}

a.with-all-transition {
  transition: 2s;
}