2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77445We extend Turaev's definition of torsion invariants of 3-dimensional manifolds equipped with non-singular vector fields, by allowing (suitable) tangency circles to the boundary, and manifolds with non-zero Euler characteristic. We show that these invariants apply in particular to (the exterior of) Legendrian links in contact 3-manifolds. Our approach uses a combinatorial encoding of vector fields, based on standard spines. In this paper we extend this encoding from closed manifolds to manifolds with boundary.30 pages, 19 figuresGeometric Topology57N10 (Primary), 57Q10, 57R25 (Secondary)text