You can add various effects to your timeline to create different transitions. For example, use a Fade effect (stretched out over time -- use the Smooth Transition button to do this automatically) to have the component fade out. Or use a Resize to have it shrink down to a pinprick. Or you can use Rotate 3D to spin it until you're viewing it edge-on (so it's just a vertical line), followed by a quick Fade out to make it fully invisible.
There's not an easy way to create a checkerboard effect, but here's one way to fake it: If you have a solid-colored background you could put a bunch of rectangles on top of the item that appear at the start of the timeline (do a quick Fade in, or Set Property visible->true), then resize until they fully cover the item.
Hope that helps,