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One key to the genera is:
Suwa, M., & B. Darvas, 1998. Family Anthomyiidae. In: Contributions to a manual of Palaearctic Diptera Volume 3 (L. Papp & B. Darvas, eds.): 571-616. Science Herald, Budapest.

And probably the key to species is:
Hennig, W., 1966-1976. 63a. Anthomyiidae. In: Die Fliegen der pal?arktischen Region 7(1) (E. Lindner, ed.): 1-974, pl. 1-78. E. Schweizerbart, Stuttgart.

I will agree immediately, not the easiest to obtain and certainly not the cheapest. Otherwise, there are few papers I am aware of. At most a species group here and there and, if you are lucky, a whole genus is treated in a journal paper.