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You can see some of the transitions in the video above.
Some included wallpapers give a distance effect. When you tilt the screen side to side and up and down, the background will shift around ever so slightly to give the screen a layer of "depth." Using the inbuilt accelerometer and compass, the wallpaper shifts beyond the edges of the screen to make the icons look like they are floating above the surface of the display.
You can also set panoramic pictures as your wallpaper.
Multitasking is much more different than in previous versions of iOS. When you double-press the home button, a stream of open apps with their corresponding icons appear. It displays what's happening on screen — live.