Any knot complement covers at most one knot complement (Q5896701)

It follows from Culler, Gordon, Luecke and Shalen's cyclic surgery theorem that any knot complement is covered by at most two knot complements. Gonzales-Acuna and Witten proved a result on the other direction: A given knot complement can cover at most finitely many knot complements. This paper is to show that the best possible result in this direction holds: A given knot complement can nontrivially cover at most one knot complement. Moreover, if the knot is not a torus knot, then the covering map is unique up to equivalence.