2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139733One method for obtaining every closed orientable 3-manifold is as branched covering of the 3-sphere over a link. There is a classical topological result showing that the minimun possible number of sheets in the covering is three. In this paper we obtain a geometric version of this result. The interest is given by the growing importance of geometry in 3-manifolds theory.18 pages, 24 figuresGeometric Topology57N10; 57M50; 57M25; 57M60; 57M10text