How to animate without miss in performance?

How to animate without miss in performance?

Inspired by this website,
www.adhamdannaway.com

i did my own version
http://americanhorizon.altervista.org/portfolio/portfolio5.php
The problem is that animation for enlarge and restrict boxes is very slow performed with jquery.
It's the only method i know to do it adding some easing effects..

If i don't use animate method all works fine, but i loose the easing effetct!!
exemple there http://americanhorizon.altervista.org/portfolio/portfolio3.php

adhamdannaway website instead uses easing without loose on perfoirmance side... How he can accomplish that?

Farther, i tryied to check the code he used, but i can't see any reference to jquery..