Annular noncrossing permutations and minimal transitive factorizations

We give two combinatorial proofs of Goulden and Jacksons formula for the number of minimal transitive factorizations of a permutation when the permutation has two cycles. We use the recent result of Goulden, Nica, and Oancea on the number of maximal chains of annular noncrossing partitions of type $B$.