You learn some thing new every dayCreate a flow path object it adds a deformer to the mesh around a curve - no fuss job done!
J
Thanks for going to all that trouble, but the motion of the animation was important.I agree the image looks to be a mess but it does nothing to show how you created the flow path object so one cannot tell what has gone wrong.
Why not just duplicate faces of the cover, scale them and then animate the verts?
Here is a crude example...
https://youtu.be/5PhcrNCc5Bo