Blow-analytic equisingularity is a relatively young branch of mathematics, it has been developed over the last three decades. This paper answers some fundamental questions raised by Kuo-Milman  and Koike (private communication). We believe that the results we present here are of interest for those working in blow-analytic equisingularity. In particular we show that the singular loci of analytic functions germs, correspond even under arc-analytic equivalences. We also give easier proofs of some results in .
"Invariants associated with blow-analytic homeomorphisms." Proc. Japan Acad. Ser. A Math. Sci. 78 (10) 194 - 198, Dec. 2002. https://doi.org/10.3792/pjaa.78.194