Although there is a small risk involved, anesthesia shouldn't be the reason why you don't want your pet neutered/spayed. The medical benefits of sterilizing your pet exceed enormously the slight risk involved with anesthetics.
Also, you can ask your veterinarian to run a pre-op checkup with your pet to ensure everything's good to go beforehand.
Source: Brown University, 2021.
Some veterinarians advise having yearly checkups to keep pets healthy. Check this article to read more: https://www.mypet.com/basic-pet-care/deserves-annual-checkup.aspx
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