word choice - Which preposition to use in “communication [over, by, through, via, with] email”?

When dealing with email, it's important to remember that it is short for "electronic mail". When trying to find the right word to use with email, drop the "e" and just consider "mail". If you do this, then "Our team kept in constant communication by mail" is the only appropriate choice. Thus, by should also be used with email.