  We have investigated the temperature and magnetic field dependence of
magnetization ($M$), specific heat ($C_p$), and relative sample length change
($\Delta L/L_0$) for understanding the field-induced metamagnetic transitions
in quasi-one-dimensional monoclinic ($\alpha$ phase) and triclinic ($\gamma$
phase) CoV$_2$O$_6$ spin chains. With the application of external magnetic
field, a sharp peak emerges in $C_p$($T$) below $T_N$$=$15 K in $\alpha$ phase
and a hump-like feature appears above $T_N$$=$6.5 K in $\gamma$ phase due to
the field-induced ferrimagnetic and ferromagnetic transitions, respectively.
Strong field dependence of linear thermal expansion and large positive
magnetostriction have been observed in $\alpha$ phase. Though magnetization
data indicate strong spin-orbit coupling for both phases, other measurements
show that this effect is very weak for the $\gamma$ phase.
