  The bipolar filtration introduced by T. Cochran, S. Harvey, and P. Horn is a
framework for the study of smooth concordance of topologically slice knots and
links. It is known that there are topologically slice 1-bipolar knots which are
not 2-bipolar. For knots, this is the highest known level at which the
filtration does not stabilize. For the case of links with two or more
components, we prove that the filtration does not stabilize at any level: for
any n, there are topologically slice links which are n-bipolar but not
(n+1)-bipolar. In the proof we describe an explicit geometric construction
which raises the bipolar height of certain links exactly by one. We show this
using the covering link calculus. Furthermore we discover that the bipolar
filtration of the group of topologically slice string links modulo smooth
concordance has a rich algebraic structure.
