  The measurements of reactions $\pi^- p \to \pi^- \pi^+ n$ and $\pi^+ n \to
\pi^+ \pi^- p$ on polarized targets at CERN found a strong dependence of pion
production amplitudes on nucleon spin. Analyses of recent measurements of
$\pi^- p \to \pi^0\pi^0 n$ reaction on unpolarized targets by GAMS
Collaboration at 38 GeV/c and BNL E852 Collaboration at 18 GeV/c use the
assumption that pion production amplitudes do not depend on nucleon spin, in
conflict with the CERN results on polarized targets. We show that measurements
of $\pi^- p \to \pi^0\pi^0 n$ and $\pi^- p \to \eta\eta n$ on unpolarized
targets can be analysed in a model independent way in terms of 4 partial-wave
intensities and 3 independent interference phases in the mass region where $S$-
and $D$-wave dominate. We also describe model-independent amplitude analysis of
$\pi^- p \to \pi^0\pi^0 n$ reaction measured on polarized target, both in the
absence and in the presence of $G$-wave amplitudes. We suggest that high
statistics measurements of reactions $\pi^- p \to \pi^0 \pi^0 n$ and $\pi^- p
\to \eta\eta n$ be made on polarized targets at Protvino IHEP and at BNL, and
that model-independent amplitude analyses of this polarized data be performed
to advance hadron spectroscopy on the level of spin dependent production
amplitudes.
