  The notions of generating sets of conservation laws of systems of
differential equations with respect to symmetry groups and equivalence groups
are introduced and applied. This allows us to generalize essentially the
procedure of finding potential symmetries for the systems with multidimensional
spaces of conservation laws. A class of variable coefficient (1+1)-dimensional
nonlinear diffusion-convection equations of general form
$f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$ is investigated. Using the most direct
method, we carry out two classifications of local conservation laws up to
equivalence relations generated by both usual and enhanced equivalence groups.
Equivalence with respect to $\hat G^{\sim}$ and correct choice of gauge
coefficients of equations play the major role for simple and clear formulation
of the final results. The notion of contractions of conservation laws and one
of characteristics of conservation laws are introduced and contractions of
conservation laws of diffusion-convection equations are found.
