Who gets the last word in emails?

I'm in PR , and today I pitched a story to a reporter who writes for my local daily and who also has a blog. She bit and wrote back, so I sent her a document, and later she emailed to tell me she posted it on her blog, so I wrote back to say thanks and happy holidays, and she wrote back to say me too.

I've stopped the back and forth now, but who should have the last word, and when do you stop thanking someone for an email greeting?

This happens a lot, when you send someone something, they write thanks, do you write back that they're welcome and so on? Is it rude not to answer every email? But if it is, when is it okay to stop replying? There must be an etiquette guide for this kind of thing.

Anyhow, happy Hanukkah and Christmas to you all. Maybe I'll get lots of comments now wishing me the same back, so I'll comment back to them, and so on, and so on.....