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This work is an extension of our previous work in \cite{bhatnagar20} tocalculate M1 transitions, $0^{-+}\rightarrow 1^{--} \gamma$, and E1 transitionsinvolving axial vector mesons such as, $1^{+-} \rightarrow 0^{-+}\gamma$, and$0^{-+}\rightarrow 1^{+-} \gamma $ for which very little data is available asof now. We make use of the general structure of the transition amplitude,$M_{fi}$ derived in our previous work \cite{bhatnagar20} as a linearsuperposition of terms involving all possible combinations of $++$, and $--$components of Salpeter wave functions of final and initial hadrons. In thepresent work, we make use of leading Dirac structures in the hadronicBethe-Salpeter wave functions of the involved hadrons, which makes theformulation more rigorous. We evaluate the decay widths for both the abovementioned $M1$ and $E1$ transitions. We have used algebraic forms of Salpeterwave functions obtained through analytic solutions of mass spectral equationsfor ground and excited states of $1^{--}$,$0^{-+}$ and $1^{+-}$ heavy-lightquarkonia in approximate harmonic oscillator basis to do analytic calculationsof their decay widths. We have compared our results with experimental data,where ever available, and other models.

$E1$ and M1 radiative transitions involving heavy-light axial, pseudoscalar and vector quarkonia in the framework of Bethe-Salpeter equation