**DIPS 6/2003**[tex source, PostScript, PDF file, dvi]-
**Title:**The long exact sequence of a covering: three applications.**Author:**I. Krasil'shchikWe construct the long exact sequence of C-cohomology associated to a covering over a differential equation E and use this sequence to solve the following problems: (1) infinitesimal description of smooth irreducible families of coverings; (2) reconstruction of nonlocal symmetries by their shadows; (3) description of action of recursion operators on (nonlocal) symmetries.

8 pages, LaTeX-2e (AmS-LaTeX).

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