I am studying an article by Livingston ("New examples of non-slice, algebraically slice knots", Proceeding of the AMS, 2001) about an example of an infinite class of knots which are algebraically slice but not slice; I recall that a knot $K$ is slice if it bounds a smooth embedded disk in $B^4$, and that it is algebraically slice if its Seifert form admits a metabolizer, which is an half-dimensional summand $H$ of the first homology group of a Seifert surface $F$ such that the restriction of the Seifert form to $H$ is null.
In the article is claimed that, given an algebraically slice knot $K$, if its metabolizer admits as a basis a link of slice knots which bound disjoint smooth embedded disks in $B^4$, then it is easily shown that $K$ is slice. Probably it is easy indeed, but I am not understanding this point. Any help (also references) would be appreciated.