2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70309We establish a calculus for branched spines of 3-manifolds by means of branched Matveev-Piergallini moves and branched bubble-moves. We briefly indicate some of its possible applications in the study and definition of State-Sum Quantum Invariants.15 pages, 12 figures. Revised version, to appear in Mathematische ZeitschriftGeometric TopologyDifferential Geometry57M20text