  A classical result by Pachner states that two $d$-dimensional combinatorial
manifolds with boundary are PL homeomorphic if and only they can be connected
by a sequence of shellings and inverse shellings. We prove that for balanced,
i.e., properly $(d + 1)$-colored, manifolds such a sequence can be chosen such
that balancedness is preserved in each step. As a key ingredient we establish
that any two balanced PL homeomorphic combinatorial manifolds with the same
boundary are connected by a sequence of basic cross-flips, as was shown
recently by Izmestiev, Klee and Novik for balanced manifolds without boundary.
Moreover, we enumerate combinatorially different basic cross-flips and show
that roughly half of these suffice to relate any two PL homeomorphic manifolds.
