Peristaltic pumps delete water when pumping left. When pumping right, there's no issue. It seems to be coded to push fluids in one direction on the grid and not the other when dealing with a sudden displacement of two water blocks and a single door block.
OK, after a bit of experimenting, doors when dealing with gases and liquids will delete part of the amount that's occupying the door if there's no empty space touching the "top" of the door (the part with the light). It looks like the base of the door marks itself empty and a solid block before the top which pushes part of the liquid into the top of the door and part into the empty space on the bottom of the door. After that, it tries to empty the top of the door, but because the bottom is now solid and each surrounding block is solid, it removes the element in the top of the door.
I set a line of doors on a system of buffers and filters so that it would activate each on a delay that would simulate wave motion to move the water. After the water is pushed to the right, it's all intact by volume. When pushed to the left, it deleted about 99% of the water present in the system. The attached video should show what it looks like in it's entirety.