If your vet thinks that the test is necessary then I would listen to your vet. The reason for the blood test is to see how the major organs are working before a general anesthetic, which is routine. A biopsy is not an operation but a simple, fast procedure by taking a small piece of skin and testing it for causes of hair loss under a microsope. It is probably a treatable condition. You will know once and for all why your cat is losing hair seasonally and get the proper treatment.
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