Sharlee --
I'm no insurance expert, but if you have been continuously covered, the new company should pick you right up. (See the "HIPPA?" thread in this forum.)
According to
this US government site , which explains the Health Insurance Portability and Accountability Act (HIPAA), your only cause for concern would be if you had gone without insurance coverage for the 63 days (or more) before the new company picked you up.
-- Leslie