  We present complete classifications of links in the 3-sphere modulo framed
and twisted Whitney towers in a rational homology 4-ball. This provides a
geometric characterization of the vanishing of the Milnor invariants of links
in terms of Whitney towers. Our result also says that the higher order Arf
invariants, which are conjectured to be nontrivial, measure the potential
difference between the Whitney tower theory in rational homology 4-balls and
that in the 4-ball extensively developed by Conant, Schneiderman and Teichner.
