Conjugacy problem in groups of oriented geometrizable 3-manifolds

The aim of this paper is to show that the fundamental group of an oriented 3-manifold which satisfies Thurston's geometrization conjecture has a solvable conjugacy problem. In other words, for any such 3-manifold M  , there exists an algorithm which can decide for any couple of elements u,vu,v of π1(M)π1(M) whether u   and vv are in the same conjugacy class of π1(M)π1(M) or not. More topologically, the algorithm decides for any two loops in M, whether they are freely homotopic or not.