On the height of 2-component links

Let p be a prime and let L be a 2-component link in S³. We define a numerical invariant, called p-height of L, using a tower of successive p-fold branched cyclic coverings of L, and show, in particular, 2-height is algorithmically determined for any 2-component link. Some relationships between p-height and known link type invariants are also established.