  In this paper, we consider the behaviour, when $q$ goes to $1$, of the set of
a convenient basis of meromorphic solutions of a family of linear
$q$-difference equations. In particular, we show that, under convenient
assumptions, such basis of meromorphic solutions converges, when $q$ goes to
$1$, to a basis of meromorphic solutions of a linear differential equation. We
also explain that given a linear differential equation of order at least two,
which has a Newton polygon that has only slopes of multiplicities one, and a
basis of meromorphic solutions, we may build a family of linear $q$-difference
equations that discretizes the linear differential equation, such that a
convenient family of basis of meromorphic solutions is a $q$-deformation of the
given basis of meromorphic solutions of the linear differential equation.
