  Bound q\bar q systems are studied in the framework of different 3-dimensional
relativistic equations derived from the Bethe-Salpeter equation with the
instantaneous kernel in the momentum space. Except the Salpeter equation, all
these equations have a correct one-body limit when one of the constituent quark
masses tends to infinity. The spin structure of the confining qq interaction
potential is taken in the form $x\gamma_{1}^{0}\gamma_{2}^{0}+(1-x)I_{1}I_{2}$,
with $0\leq x \leq 1$. At first stage, the one-gluon-exchange potential is
neglected and the confining potential is taken in the oscillator form. For the
systems (u\bar s), (c\bar u), (c\bar s) and (u\bar u), (s\bar s) a comparative
qualitative analysis of these equations is carried out for different values of
the mixing parameter x and the confining potential strength parameter. We
investigate: 1)the existence/nonexistence of stable solutions of these
equations; 2) the parameter dependence of the general structure of the meson
mass spectum and leptonic decay constants of pseudoscalar and vector mesons. It
is demonstrated that none of the 3-dimensional equations considered in the
present paper does simultaneously describe even general qualitative features of
the whole mass spectrum of q\bar q systems. At the same time, these versions
give an acceptable description of the meson leptonic decay characteristics.
