This paper reports on our diagrammatic approach to characterize the gauge dependence of Quantum Electrodynamics in the linear covariant gauge. Our dimensionally independent technique is purely based on a perturbative analysis and allows us to construct the full expansion in the gauge~parameter of a Green's function from its value in a particular gauge (such as the Feynman or Landau gauge). Further, we clarify the compatiblity of perturbation theory and the Landau-Khalatnikov-Fradkin transform.