Is it a good idea to use neosporin for opened blisters?
Example of opened blisters:
As per its description, Neosporin can be used for minor cuts and scrapes, which seem to fit well to your description of opened blister.
The picture provided shows a shallow opening. I doubt something like that would be much of a concern. It would be better to cleanly cut of the loose cut skin to a comfortable level and wait for the healing process to complete. If the loose skin is left uncut, it would have the risk of becoming a handle to rip the skin further. If the wound is deeper, then treat the wound as prescribed.
See this from the AAD about wound care.
See this from Medscape for interesting info on wound healing.