How to continue material between sprites.

I have levels made up of objects of different size and shape and I would like to apply my shader material to all of them in a way that it continues from object to object instead of restarting at each, which produces unappealing transitions:

In this case I would like blue blocks to have a smooth transition as if it was one game object.

My idea was to make one big sprite behind them and apply shader to it, while these objects will somehow be windows to it, but not quite sure how that could be implemented.