We have investigated the thermally activated behavior of the in-plane electrical resistivity of Bi 2 Sr 2 CaCu 2 O 8ϩ␦ films for magnetic fields Bр10 4 G applied parallel to the c axis. The activation energy in the vortex-liquid state changes suddenly at a crossover field B cr . The anisotropy reduction generated by oxygen annealing leads to the increase of the crossover field. For BϽB cr , the activation energy U is weakly magnetic-field dependent. For BϾB cr , U(B,T)ϳ(1ϪT/T c0 )/B 1/2 , which corresponds to an entangled vortex fluid. The observation of vortex-liquid entanglement in the presence of relevant quenched disorder is discussed in connection with the relation between the theoretically predicted entanglement length for a clean system and the collective pinning length along the field direction. Our results suggests that, in the case of a pronounced anisotropy and significant collective pinning, the entanglement field B E ϭB cr Ϸ⌽ 0 /␥ 2 s 2 , where s is the interlayer spacing.