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
[10] 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 [1].