  This paper discusses the dynamics of continuum-wise hyperbolic surface
homeomorphisms. We prove that $cw_F$-hyperbolic surface homeomorphisms
containing only a finite set of spines are $cw_2$-hyperbolic. In the case of
$cw_3$-hyperbolic homeomorphisms we prove the finiteness of spines and, hence,
that $cw_3$-hyperbolicity implies $cw_2$-hyperbolicity. In the proof, we adapt
techniques of Hiraide [11] and Lewowicz [15] in the case of expansive surface
homeomorphisms to prove that local stable/unstable continua of
$cw_F$-hyperbolic homeomorphisms are continuous arcs. We also adapt techniques
of Artigue, Pac\'ifico and Vieitez [6] in the case of N-expansive surface
homeomorphisms to prove that the existence of spines is strongly related to the
existence of bi-asymptotic sectors and conclude that spines are necessarily
isolated from other spines.
