  We investigate the self-consistency and Lorentz covariance of the covariant
light-front quark model~(CLF QM) via the matrix elements and form
factors~(${\cal F}=g$, $a_{\pm}$ and $f$) of $P\to V$ transition. Two types of
correspondence schemes between the manifest covariant Bethe-Salpeter approach
and the light-front quark model are studied. We find that, for $a_{-}(q^2)$ and
$f(q^2)$, the CLF results obtained via $\lbd=0$ and $\pm$ polarization states
of vector meson within the traditional type-I correspondence scheme are
inconsistent with each other; and moreover, the strict covariance of the matrix
element is violated due to the nonvanishing spurious contributions associated
with noncovariance. We further show that such two problems have the same origin
and can be resolved simultaneously by employing the type-II correspondence
scheme, which advocates an additional replacement $M\to M_0$ relative to the
traditional type-I scheme; meanwhile, the results of ${\cal F}(q^2)$ in the
standard light-front quark model~(SLF QM) are exactly the same as the valence
contributions and equal to numerally the full results in the CLF QM, {\it
i.e.}, $[{\cal{F}}]_{\rm SLF}=[{\cal{F}}]_{\rm val.}\doteq[{\cal{F}}]_{\rm
full}$. The numerical results for some $P\to V$ transitions are updated within
the type-II scheme. Above findings confirm the conclusion obtained via the
decay constants of vector and axial-vector mesons in the previous works.
