High-energy peripheral reactions provide an excellent opportunity to
study the excitation spectrum of hadrons. The COMPASS experiment at
CERN has measured the diffractive scattering of pions to the 3-pion
final state with unprecedented statistical precision. Partial wave
analysis techniques have been employed to obtain an expansion of the
reaction cross section in terms of partial waves with quantum numbers
J^PC M^epsilon.

Since around a hundred of observed resonances in the light sector are
coupled to pionic systems, the spin-density matrices from COMPASS PWA
are extremely valuable data to identify ordinary and, possibly, exotic
mesons. One very interesting candidate to the latter is a
resonance-like behaviour in the 1++ 0+ f_0 pi P-wave which has
been listed in the latest PDG as a_1(1420).

The aim of our analysis is an extraction of three pion scattering
amplitudes from mass-dependence of the COMPASS spin-density matrices
using analyticity and unitarity constraints.

First I am considering the isobar model and the quasi-two-body unitarity.
Using K-matrix approach, we built the amplitude for scattering of a
quasi-two-body final state (pi pi-subchannnel resonance + pion),
and include a unitarization procedure to incorporate non-resonant
long-range production processes via pion exchange, i.e. ``Deck''-like
processes. An application of the model to 2-+ sector will be
shown.

The second part will be dedicated to a_1(1420) phenomenon. We show
that the peculiar kinematics of pi pi pi - Kbar K pi rescattering
for the invariant mass around 1.4 GeV produces the resonance-like
behaviour. A mechanism called Triangle Singularity is likely
responsible for the a_1(1420) appearance. I will discuss a
systematic way to deal the rescattering.