Approximation of sets defined by polynomials with holomorphic coefficients

Let X be an analytic set defined by polynomials whose coefficients a_1,…,a_s are holomorphic functions. We formulate conditions such that for all sequences {a_(1,n)},…,{a_(s,n)} of holomorphic functions converging locally uniformly to a_1,…,a_s respectively the following holds true. If a_(1,n),…,a_(s,n) satisfy the conditions then the sequence of the sets {X_n} obtained by replacing a_j by a_(j,n) in the polynomials, converge to X.