In the Kirby list is presented the following problem: describe the
equivalence classes in the set of knots under the relation K$_{1}$
is equivalent to K$_{2}$ if their 2-fold cyclic branched coverings
are homeomorphic 3-manifolds. In this paper we consider the basic
case of hyperbolic manifold. In the fi{}rst part of this paper we
want to present briefl{}y the results, yet available in some previous
works, which solve this problem. In the second part we present examples
of knots with the same 2-fold branched covering which show that the
theorem, which describes the possible relations between two knots
in the same equivalence class, is the best possible.
