In the context of non-perturbative studies of the Schwinger-Dyson equations (SDEs), the complete determination of a Quantum field theory and its corresponding physical observables requires in principle the knowledge of the full set of Green functions associated. In order to reduce the infinite tower of coupled SDEs to a practically solvable set, one must find a systematic scheme of truncation, preserving the symmetries of the theory. An usual practice is to make an Ansatz for the three point fermion-boson vertex. Quantum electrodynamics (QED) is an illuminating example in which we can study the constraints of gauge invariance, namely, the Ward-Fradkin-Green-Takahashi identities (WFGTI), which determine the so called longitudinal part of this vertex and the Landau-Khalatnikov-Fradkin transformations (LKFT), which probe its component transverse to the photon momentum and undetermined by the WFGTI. We employ the transverse Takahashi identities (TTI) to impose further non perturbative constraints on the transverse part of the three-point fermion-boson vertex. We show that implementation of these identities is crucial in ensuring the correct local gauge transformation for the electron propagator and its multiplicative renormalizability. We also make an explicit comparison of various existing constructions of this vertex against the demands of the TTI.