  The fermion propagator in an arbitrary covariant gauge can be obtained from
the Landau gauge result via a Landau-Khalatnikov-Fradkin transformation. This
transformation can be written in a practically useful form in both
configuration and momentum space. It is therefore possible to anticipate
effects of a gauge transformation on the propagator's analytic properties.
These facts enable one to establish that if a critical number of flavours for
chiral symmetry restoration and deconfinement exists in noncompact QED3, then
its value is independent of the gauge parameter. This is explicated using
simple forms for the fermion-photon vertex and the photon vacuum polarisation.
The illustration highlights pitfalls that must be avoided in order to arrive at
valid conclusions. Landau gauge is seen to be the covariant gauge in which the
propagator avoids modification by a non-dynamical gauge-dependent exponential
factor, whose presence can obscure truly observable features of the theory.
