If I start w/ a new health insurance provider on Jan 1st will the previous provider cover bills before then?

I had a hospital bill and other doctors bills from a few weeks ago. If they're not paid right away by my current provider will they still handle them since the services took place before the Dec 31st expiration date?
--------------------
Yes. For medical office visits, hospital visits, and medical procedures, the date of service is the key determiner. The insurance in effect on the date of service, would be the one that pays on the bill. Most insurance claims for medical, can be filed up to a year after the date of service. Some carriers have a shorter period. For many medical procedures it takes a few days at least to prepare the insurance claim, so this kind of processing is routine for doctors and insurance companies.
Source