Should be a straightforward matter of having each cutout piece as a separate layer then transition these in as you see fit.
If you want an interesting wipe effect then Add a Layer Mask to each layer, set it to Luma. Then create an interesting gradient, and set this as the layer mask for your cutout layer (just drag and drop it into the image mask layer). Finally add a Brightness/Contrast filter (to your grad) and play away.
Lather rinse repeat for the other layers.
That should do it for you. There are, of course, other ways to achieve the same effect.
Cheers,
Ben
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