INR and blood clots. What if the clots happen during the surgery?

My INR show .95 which according to my primary doctor is too low. He explained to me that I am at a high risk of blood clots during a lipo, however my surgeon doesn’t seen worry. He said he’ll give me blood thinner after the surgery. But with this condition and my family history of blood clots, why he can’t give it to me prior to surgery? What if the clots happens during the surgery and I die? I think is better to bleed a lot during surgery than to have blood clots.

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