Let K be a knot in S³, and M and M' be distinct Dehn surgeries along K. We investigate when M covers M'. When K is a torus knot, we provide a complete classification of such covers. When K is a hyperbolic knot, we provide partial results in the direction of the conjecture that M never covers M'.

I would like to thank the referee on a previous version for useful comments, Nathan Dunfield, Jessica Purcell, and Cameron Gordon for helpful conversations, and Robert Lipshitz for support, suggestions, and corrections.