  For any Nambu-Jona-Lasinio model of QCD with arbitrary nonlocal,
instantaneous, quark current-current confining kernels, we use a generalised
Bogoliubov technique to go beyond BCS level (in the large-Nc limit) so as to
explicitly build quark-antiquark compound operators for creating/annihilating
mesons. In the Hamiltonian approach, the mesonic bound-state equations appear
(from the generalised Bogoliubov transformation) as mass-gap-like equations
which, in turn, ensure the absence, in the Hamiltonian, of mesonic Bogoliubov
anomalous terms. We go further to demonstrate the one-to-one correspondence
between Hamiltonian and Bethe-Salpeter approaches to non-local NJL-type models
for QCD and give the corresponding "dictionary" necessary to "translate" the
amplitudes built using the graphical Feynman rules to the terms of the
Hamiltonian, and vice versa. We comment on the problem of multiple vacua
existence in such type of models and argue that mesonic states in the theory
should be prescribed to have an extra index - the index of the replica in which
they are created. Then the completely diagonalised Hamiltonian should contain a
sum over this new index. The method is proved to be general and valid for any
instantaneous quark kernel.
