  Based on an exact formulation, we present a master equation approach to
transport through Majorana zero modes (MZMs). Within the master equation
treatment, the occupation dynamics of the regular fermion associated with the
MZMs holds a quite different picture from the BdG S-matrix scattering process,
in which the "positive" and "negative" energy states are employed, while the
master equation treatment does not involve them at all. Via careful analysis
for the structure of the rates and the rate processes governed by the master
equation, we reveal the intrinsic connection between both approaches. This
connection enables us to better understand the confusing issue of teleportation
when the Majorana coupling vanishes. We illustrate the behaviors of transient
rates, occupation dynamics and currents. Through the bias voltage dependence,
we also show the Markovian condition for the rates, which can extremely
simplify the applications in practice. As future perspective, the master
equation approach developed in this work can be applied to study important
time-dependent phenomena such as photon-assisted tunneling through the MZMs and
modulation effect of the Majorana coupling energy.
