I prefer to pull my blocks when I cut the hole and place them back in when I'm done. I then mark the edges of the hole with pine branches. If I have to push the blocks under I mark the hole by surrounding it with the pine branches.
I always seem to hear a lot complaints every year from people about unmarked open holes and cut blocks left on top of the ice. Both are definite problems with the potential for a person stepping into a partially frozen hole hidden by a skiff of snow to a snowmobile or quad driver running into the blocks.