I didn't include animations, but this should do exactly what you're looking for.
<style>
#background {
height: 100px;
width: 100px;
background-img:('foo.png')}
#background.hover1{background-position:0px 0px}
#background.hover2{background-position:0px 100px}
#background.hover3{background-position:0px 200px}
#background.hover4{background-position:0px 300px}
</style>
<div id="background"></div>
<a id="hover1" class="trigger" href="#">State 1</a>
<a id="hover2" class="trigger" href="#">State 2</a>
<a id="hover3" class="trigger" href="#">State 3</a>
<a id="hover4" class="trigger" href="#">State 4</a>
<script>
$(".trigger").hover(function (){
// get hover class
var hoverClass = $(this).attr('id');
// remove active class from any trigger link
$(".trigger").removeClass('active');
// add active class to current trigger link
$(this).addClass('active');
// add hover class to the background div to shift the background position
$("#background").removeClass().addClass(hoverClass);
});
</script>