On Milnor's invariants of 4-component links

We study the behavior of Milnor's mu-invariants of three- and four-component links with respect to the discriminant determined by Delta-moves of links. We introduce a new type of Delta-move, balanced Delta-moves, or, briefly, BDelta-moves. Since each four-component link is equivalent to a standard link under a sequence of balanced Delta-moves, Delta-moves that involve at most two components, and Reidemeister moves, we manage to define axiomatically mu-invariants of length 3 for arbitrary semibounding links.