  We construct a global Lindblad master equation for a Kitaev quantum wire of
finite length, weakly coupled to an arbitrary number of thermal baths, within
the Born-Markov and secular approximations. We find that the coupling of an
external bath to more than one lattice site generates quantum interference
effects, arising from the possibility of fermions to tunnel through multiple
paths. In the presence of two baths at different temperatures and/or chemical
potentials, the steady-state particle current can be expressed through the
Landauer-B\"uttiker formula, as in a ballistic transport setup, with the
addition of an anomaly factor associated with the presence of the $p$-wave
pairing in the Kitaev Hamiltonian. Such a factor is affected by the
ground-state properties of the chain, being related to the finite-size
equivalent of its Pfaffian topological invariant.
