  We study theoretically the nonlinear interactions of vector breathers
propagating on an unstable wavefield background. As a model, we use the
two-component extension of the one-dimensional focusing nonlinear Schrodinger
equation -- the Manakov system. With the dressing method, we generate the
multi-breather solutions to the Manakov model. As shown previously in [D.
Kraus, G. Biondini, and G. Kovacic, Nonlinearity 28, 310, 2015] the class of
vector breathers is presented by three fundamental types I, II, and III. Their
interactions produce a broad family of the two-component (polarized) nonlinear
wave patterns. First, we demonstrate that the type I and the types II and III
correspond to two different branches of the dispersion law of the Manakov
system in the presence of the unstable background. Then we investigate the key
interaction scenarios, including collisions of standing and moving breathers
and resonance breather transformations. Analysis of the two-breather solution
allows us to derive general formulas describing phase and space shifts acquired
by breathers in mutual collisions. The found expressions enable us to describe
the asymptotic states of the breather interactions and interpret the resonance
fusion and decay of breathers as a limiting case of infinite space shift in the
case of merging breather eigenvalues. Finally, we demonstrate that only type
$\mathrm{I}$ breathers participate in the development of modulation instability
from small-amplitude perturbations within the superregular scenario, while the
breathers of types $\mathrm{II}$ and $\mathrm{III}$, belonging to the stable
branch of the dispersion law, are not involved in this process.
