  A four-body amplitude analysis of the $B^- \to D^{*+} \pi^- \pi^-$ decay is
performed, where fractions and relative phases of the various resonances
contributing to the decay are measured. Several quasi-model-independent
analyses are performed aimed at searching for the presence of new states and
establishing the quantum numbers of previously observed charmed meson
resonances. In particular the resonance parameters and quantum numbers are
determined for the $D_1(2420)$, $D_1(2430)$, $D_0(2550)$, $D^*_1(2600)$,
$D_2(2740)$ and $D^*_3(2750)$ states. The mixing between the $D_1(2420)$ and
$D_1(2430)$ resonances is studied and the mixing parameters are measured. The
dataset corresponds to an integrated luminosity of 4.7 $fb^{-1}$, collected in
proton-proton collisions at center-of-mass energies of 7, 8 and 13 TeV with the
LHCb detector.
