If a nontrivial knot admits purely cosmetic surgeries, then some hyperbolic knot also does, reducing the cosmetic surgery conjecture to the hyperbolic case.
Berge, The knots in D2 × S1 which have nontrivial Dehn surgeries that yield D2 × S1, Topology Appl
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Cosmetic surgery on satellite knots
If a nontrivial knot admits purely cosmetic surgeries, then some hyperbolic knot also does, reducing the cosmetic surgery conjecture to the hyperbolic case.