After looking at the source code on the site, I believe the slide show is made by THEMEPUNCH TOOLS. It also mentions Wait For Images to load the image events and jQuery Transit for smooth CSS animations.
In terms of getting the layered animations, I believe all but 1 (the Howard & Stein slide) slide had the same pattern of animation, meaning it's likely 1 script that's causing the animation within each slide. If you want each slide to have a different pattern of animation, you're going to have to write separate scripts. Alternatively, you can check out those links to animate your own content.