Two branched covers of the three-sphere over a stably Chebotarev link are homeomorphic if and only if their absolute Galois groups are isomorphic via a characteristic-preserving isomorphism.
Poitou.Cohomologie galoisienne des modules finis, volume No
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A Neukirch-Uchida Theorem for 3-Manifolds
Two branched covers of the three-sphere over a stably Chebotarev link are homeomorphic if and only if their absolute Galois groups are isomorphic via a characteristic-preserving isomorphism.