"emailing back and forth" is correct and usable in written English. You can use it to describe a situation in which two or more people repeatedly email each other. For example, "John and Sarah had been emailing back and forth for weeks before finally deciding to meet in person.".
"We have been emailing back and forth a little.
Aaron Carroll of The Incidental Economist and I have been emailing back and forth about the extent to which conservative states tend to be much more dependent on government support than liberal states, and Aaron has produced a nice chart.
We've been emailing back and forth with Google since Wednesday but so far they haven't said what it is.
That means users don't have to spend days emailing back and forth with a vacation rental owner to arrange a transaction and a stay.
Our work always starts with a germination period, in which Damon and I might talk or email back and forth, telling each other stories about our own lives, and eventually out of that might come an idea.
I discovered a really interesting piece on alchemy and emailed it to Carina with the message: "I've been thinking about our book…" We emailed back and forth all that day – links to 15th-century books by Vatican witch hunters, modern day dissertations on ancient beliefs, alchemical texts, and ideas about our characters.
In recent studies pdf surveys that can be emailed back and forth between the researchers and the SPOCs have been usedq.
When I feel like I can't trust my brain 100%, Ludwig really comes in handy. It makes me translate and proofread faster and my output more reliable.
Claudia Letizia
Head Translator and Proofreader @ organictranslations.eu