  In the context of a SUSY GUT inspired MSSM version, the low energy
consequences of the asymptotic $b-\tau$ Yukawa coupling Unification are
examined, under the assumption of universal or non-universal boundary
conditions for the gaugino and sfermion masses. Gaugino non-universality is
applied, so that the SUSY corrections to $b$-quark mass can be reconciled with
the present experimental data on muon anomalous magnetic moment. Restrictions
on the parameter space, originating from the Cold Dark Matter abundance in the
universe, the inclusive branching ratio of $b\to s\gamma$ and the accelerator
data are, also, investigated and the scalar neutralino-proton cross section is
calculated. In the case of a bino-like LSP and universal boundary conditions
for the sfermion masses, the constraints, arising from the Cold Dark Matter and
${\rm BR}(b \to s\gamma)$ can be simultaneously satisfied, mainly thanks to the
$A$-pole effect or the neutralino-stau coannihilations. In addition, sfermion
mass non-universality provides the possibility of new coannihilation phenomena
(neutralino-sbottom or neutralino-tau sneutrino-stau), which facilitate the
simultaneous satisfaction of all the above requirements. In both cases above,
the neutralino abundance can essentially decrease for a W-ino or higgsino like
LSP creating regions of parameter space with additional neutralino-chargino
and/or heavier neutralino coannihilations. The neutralino-sbottom mass
proximity significantly ameliorates the detectability of LSP.
