The phrase "to handle the anesthetic" means to manage or take care of the administration and use of a substance that numbs pain during medical procedures. Full definition
Animals that have minor dysfunctions will handle the anesthetic better if they receive IV fluids during surgery. (northviewpetcare.com)
This is especially important to test before going under an anesthetic procedure to make sure the body will be able to handle the anesthetics in its system. (kmvet.com)
Animals that have minor problems will handle the anesthetic better if they receive IV fluids during surgery. (countrycourtanimalhospital.com)