TITLE: Reference for a theorem on crossing changes of links
QUESTION [5 upvotes]: I've recently stumbled upon a paper of Scharlemann on crossing changes: 
link text
In particular I am interested in understanding Theorem 2.2 (page 6):
"Theorem: If links A and B
are related by a crossing change, and both are composite,
then the crossing change takes place within a proper summand."
Where can I find a proof of this result?
Also, is it possible to find an equivalent statement on diagrams?
Thanks

REPLY [2 votes]: The reference is given in the paper you cite:
M. Eudave-Mun ̃oz, Primeness and sums of tangles, Trans. Am. Math. Soc. 306, 773-790 (1988)
The arguments are purely combinatorial, but there should be a simplification using sutured manifold theory along the lines of Scharlemann and Thompson's paper "Unknotting number, genus, and companion tori" by Scharlemann and Thompson MR0929535
Off the top of my head, I don't see a way to convert either type of argument into a something about diagrams.