We present an exhaustive analysis of transport measurements performed in twinned YBa2Cu3O7 single crystals which stablishes that the vortex solid-liquid transition is first order when the magnetic field H is applied at an angle theta away from the direction of the twin planes. We show that the resistive transitions are hysteretic and the V-I curves are non-linear, displaying a characteristic s-shape at the melting line Hm(T), which scales as epsilon(theta)Hm(T,theta). These features are gradually lost when the critical point H*(theta) is approached. Above H*(theta) the V-I characteristics show a linear response in the experimentally accessible V-I window, and the transition becomes reversible. Finally we show that the first order phase transition takes place between a highly correlated vortex liquid in the field direction and a solid state of unknown symmetry. As a consequence, the available data support the scenario for a vortex-line melting rather than a vortex sublimation as recently suggested [T.Sasagawa et al. PRL 80, 4297 (1998)].