  We study the gauge covariance of the fermion propagator in
Maxwell-Chern-Simons planar quantum electrodynamics (QED$_3$) considering
four-component spinors with parity-even and parity-odd mass terms both for
fermions and photons. Starting with its tree level expression in the Landau
gauge, we derive a non perturbative expression for this propagator in an
arbitrary covariant gauge by means of its Landau-Khalatnikov-Fradkin
transformation (LKFT). We compare our findings in the weak coupling regime with
the direct one-loop calculation of the two-point Green function and observe
perfect agreement up to a gauge independent term. We also reproduce results
derived in earlier works as special cases of our findings.
