"Email conversation" refers to an exchange of messages between people through email, similar to having a conversation but using written electronic communication instead of speaking. Full definition
Many customers have complained online about weeks - long email conversations with representatives for issues which only got resolved when the customer took the issue public on forums or in the press. (businessinsider.my)
You can receive emails and respond to emails but you can not initiate email conversations. (blackwhitedatingreviews.com)
The personal contact may actually reduce or replace the need for long email conversations. (inc.com)