The easing breaks every time AnythingSlider is forced to "rotate" its pages. (Put another way: any time the item being moved to is a "li.cloned", the easing is broken.)
It looks to me like this is a bug within AnythingSlider, I think some of the animation-complete callbacks are being called without waiting for animation to actually complete.
I hesitate to analyze any further because the current site is using version 1.2 of AnythingSlider, latest version is v1.5.x. I would try upgrading and see if that fixes your problem.
https://github.com/ProLoser/AnythingSlider/downloads