  This letter examines diagrammatic cancellations for Quantum Electrodynamics
(QED) in the general linear gauge. These cancellations combine Feynman graphs
of various topologies and provide a method to reconstruct the gauge dependence
of the electron propagator from the result of a particular gauge by means of a
linear Dyson-Schwinger equation. We use this method in combination with
dimensional regularization to demonstrate how the 3-loop ${\epsilon}$-expansion
in the Feynman gauge determines the ${\epsilon}$-expansions for all gauge
parameter dependent terms to 4 loops.
