  We study the question of complete gauge independence of the fermion pole mass
by choosing a general class of gauge fixing which interpolates between the
covariant, the axial and the Coulomb gauges for different values of the gauge
fixing parameters. We derive the Nielsen identity describing the gauge
parameter variation of the fermion two point function in this general class of
gauges. Furthermore, we relate the denominator of the fermion propagator to the
two point function. This then allows us to study directly the gauge parameter
dependence of the denominator of the propa- gator using the Nielsen identity
for the two point function. This leads to a simple proof that, when infrared
divergences and mass shell singularities are not present at the pole, the
fermion pole mass is gauge independent, in the complete sense, to all orders in
perturbation theory. Namely, the pole is not only independent of the gauge
fixing parameters, but has also the same value in both covariant and
non-covariant gauges.
