  The Landau-Khalatnikov-Fradkin transformations (LKFTs) represent an important
tool for probing the gauge dependence of the correlation functions within the
class of linear covariant gauges. Recently these transformations have been
derived from first principles in the context of non-Abelian gauge theory (QCD)
introducing a gauge invariant transverse gauge field expressible as an infinite
power series in a Stueckelberg field. In this work we explicitly calculate the
transformation for the gluon propagator, reproducing its dependence on the
gauge parameter at the one loop level and elucidating the role of the extra
fields involved in this theoretical framework. Later on, employing a unifying
scheme based upon the BRST symmetry and a resulting generalized Slavnov-Taylor
identity, we establish the equivalence between the LKFTs and the Nielsen
identities which are also known to connect results in different gauges.
