  We study by means of the recursive Green's function technique the local
density-of-states of (finite and semi-infinite) multi-band spin-orbit coupled
semiconducting nanowires in proximity to an s-wave superconductor and attached
to normal-metal electrodes. When the nanowire is coupled to a normal electrode,
the zero-energy peak, corresponding to the Majorana state in the topological
phase, broadens with increasing transmission between the wire and the leads,
eventually disappearing for ideal interfaces. Interestingly, for a finite
transmission a peak is present also in the normal electrode, even though it has
a smaller amplitude and broadens more rapidly with the strength of the
coupling. Unpaired Majorana states can survive close to a topological phase
transition even when the number of open channels (defined in the absence of
superconductivity) is even. We finally study the Andreev-bound-state spectrum
in superconductor-normal metal-superconductor junctions and find that in
multi-band nanowires the distinction between topologically trivial and
non-trivial systems based on the number of zero-energy crossings is preserved.
