  Based on the analogy between knots and primes, J. Hillman, D. Matei and M.
Morishita defined the Iwasawa invariants for sequences of cyclic covers of
links with an analogue of Iwasawa's class number formula of number fields. In
this paper, we consider the existence of covers of links with prescribed
Iwasawa invariants, discussing analogies in number theory. We also propose and
consider a problem analogous to Greenberg's conjecture.
