The author defines virtual Betti numbers and a virtual Euler characteristic for real constructible arc-symmetric sets, and respectively an analogue of the Denef-Loeser motivic zeta-function, motivic Poincaré polynomial. It is proven that these objects are invariants with respect to the blow-Nash equivalence. As application, the author gives the blow-Nash classification of Brieskorn polynomials in two variables, and also shows that the blow-Nash equivalence in algebraic families with isolated singularities has no moduli.