Topological equivalence of complex polynomials

The following numerical control over the topological equivalence is proved: two complex polynomials in $n≠3$ variables and with isolated singularities are topologically equivalent if one deforms into the other by a continuous family of polynomial functions $f_s\text{\hspace{0.17em}⁣}:{\mathbb{C}}^n\to \mathbb{C}$ with isolated singularities such that the degree, the number of vanishing cycles and the number of atypical values are constant in the family.