2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62244A combinatorial presentation of closed orientable 3-manifolds as bi-tricolored links is given together with two versions of a calculus via moves to manipulate bi-tricolored links without changing the represented manifold. That is, we provide a finite set of moves sufficient to relate any two manifestations of the same 3-manifold as a simple 4-sheeted branched covering of S^3.63 pages, lots of pstrics and some xypic pictures, based on the author's PhD thesis at GC of CUNYGeometric Topology57M12; 57M25text