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Explanation: slightly more formal than "file" perhaps.
As for "deed", it depends on the kind of "atto" we're dealing with. Usually the word is used in the plural (deeds) to mean a signed agreement, especially to do with the ownership of property or legal rights. It could be a certificate, a document, but certainly not an "act" which in a legal context is a term reserved to laws passed by Parliament or to... God!