  Scattering theory has been suggested as a convenient method to identify
topological phases of matter, in particular of disordered systems for which the
Bloch band-theory approach is inapplicable. Here we examine this idea,
employing as a benchmark a one-dimensional triangle chain whose versatility
yields a scattering matrix that ``flows" in parameter space among several
members of the topology classification scheme. Our results show that the
reflection amplitudes (from both ends of a sufficiently long chain) do indicate
the appearance of edge states in {\it all} (topological and non-topological)
cases. For the topological cases, the transmission has a peak at the
topological phase transition, which happens at the Fermi energy. A peak still
exists as one moves into the non-topological `trivial' regions, in which
another transmission peak may occur at nonzero energy, at which a relevant edge
state appears in the isolated chain. For finite chains, the peak in the
transmission strongly depends on their coupling of the leads, and {\it not} on
the phase transition of the isolated chain. In any case, {\it the appearance of
a peak in the transmission is not sufficient to conclude that the system
undergoes a topological phase transition.}
