Can a vet tech open up an animal hospital?

It will depend on the state that the veterinary facility is in and the exact nature of the relationship between the veterinary technician and the veterinary practice. Some states do not allow anyone but a veterinarian to open a veterinary practice. It may be possible, however, for a veterinary technician to own the facilities and employ the veterinary staff which they contract out to a veterinarian. In these situations, the veterinarian owns the practice (client records, makes all medical decisions, etc) and rents property and staff from the facility owner.