Witten-type interaction of strings with unequal lengths

A BRS-invariant (in 26 dimensions) three-string vertex, extending Witten's one to strings of different lengths, is constructed. The ''joining-and-splitting'' picture corresponds to a singular limit in the space of string-length parameters. Independence of S-matrix elements with respect to the latter is checked explicitly in the case of the on-shell tachyon-tachyon-vector amplitude