An important point when deleting a Hyper-V snapshot is that the corresponding AVHD file isn’t merged into the main VHD file until you power down the server.  This means that the disk space used by the snapshot isn’t immediately available when you delete a snapshot.

As far as I’m aware there’s no way to monitor the merge process through System Center Virtual Machine Manager, but you can via the Hyper-V MMC.

If you start a virtual machine during the merge process, the merge process stops and the machine starts instantly.