  We consider the $3$D problem of shape optimization of blood flows in moving
domains. Such a geometry is adopted to take into account the modeling of
rotating systems and blood pumps for instance. The blood flow is described by
generalized Navier-Stokes equations, in the particular case of shear-thinning
flows. For a sequence of converging moving domains, we show that a sequence of
associated solutions to blood equations converges to a solution of the problem
written on the limit moving domain. Thus, we extended the result given in
(Soko\l{}owski, Stebel, 2014, in \textit{Evol. Eq. Control Theory}) for $q \geq
11/5$, to the range $6/5< q < 11/5$, where $q$ is the exponent of the
rheological law. This shape continuity property allows us to show the existence
of minimal shapes for a class of functionals depending on the blood velocity
field and its gradient. This allows to consider in particular the problem of
hemolysis minimization in blood flows, namely the minimization of red blood
cells damage.
