Updated your example to use CSS3 animations as that's the way to go nowadays. No javascript needed, better performance and graceful degradation for free!
.next,
.prev {
opacity: 0;
transition: opacity .25s ease-in-out;
-moz-transition: opacity .25s ease-in-out;
-webkit-transition: opacity .25s ease-in-out;
}
.image_carousel:hover .next,
.image_carousel:hover .prev {
opacity: 1;
}