Eviction - What happens if tenant pays rent after I filed papers

[Chris Weike]

I have these tenants who constantly pay late (like 2 weeks late). Last month I put a '3 Day Notice' on their door and they paid immediately.  This month they texted that they don't care about the notice, and I should just put it on their door again. I know I'd stop the eviction process after they pay rent in full, but what happen after the 3 days. If I go to court and file the unlawful detainer, pay the fees due (not cheap in CA), and serve the tenant and then he decides to pay his rent - will I be able to continue the eviction, or do I have to stop, lose the fees I paid and do it all over again next month? It's a cat and mouse game and the tenant might just like that and enjoys me paying hundreds in fees every month for filing papers. Any advice or someone who has been in a similar situation?

These tenants have funds, but are completely unorganized and have some family drama.