I find some (young?) people say ちげー when they mean 違う. Is there other verb that is frequently sound-reduced? (BTW, what is the correct way to describe this phonological phenomenon or the word for this kind of phonological change?)
I think this is a variant of the /ai/-to-/ee/ sound change that typically happens with i-adjectives:
If I understand correctly, in the past, ちげぇ (also written as ちげー or ちげえ) happened only when ちがう conjugated to the continuative form, ちがい (chigai). For example, speakers of Tokyo Shitamachi dialect have long said ちげぇます instead of ちがいます, or ちげぇねぇ instead of ちがいない. Likewise, it has been always possible to contract 笑います to われぇます, 歌いたい to うてぇてぇ, and so on.
However, this still does not explain why ちがう (chigau) followed by nothing became ちげぇ. Some young people do say ちげぇ instead of ちがう today, although no one says うてぇ instead of うたう.
I think this phenomenon is unique to 違う, and is related to the recent peculiar (mis)use of 違う. In today's nonstandard slang, 違う occasionally conjugates like an adjective, as if there were an i-adjective 違い. Have you ever seen 違くない, 違くて or 違かった used by young speakers? These are definitely nonstandard, but for those who feel they are natural, saying ちげぇ instead of ちがう should be natural, too, because their brains recognize the word ちがい as an adjective. (Of course they are not consciously aware of this.)