Move your pets to a relative or friend’s house. I know that this can be heart breaking, but even the most well behaved pet leaves behind fur and odors. You don’t want to spend hours shampooing your rugs and cleaning your furniture just to have them covered in fur. Or must worse to have your home smell like your much loved, but stinky, pet.
Even worse, your pet will leave behind dander, the leading cause of animal allergies. No one is even going to walk through a home in which they cannot breathe. So move your pets out of your home before you do your cleaning, and keep them out until after you move.