Changing jobs with an H1-B visa type

I am wondering if there is a grace period for filing the I129 petition with INS if I get a new job (and sponsor) while working under H1-B status. Can the petition be filed after leaving the company of the previous sponsor. Also,if the DOJ approves the request, can I begin working with the new company/sponsor before the actual visa is delivered?

Thank you in advance for any assistance.

I am wondering if there is a grace period for filing the I129 petition with INS if I get a new job (and sponsor) while working under H1-B status. Can the petition be filed after leaving the company of the previous sponsor. Also,if the DOJ approves the request, can I begin working with the new company/sponsor before the actual visa is delivered?

Thank you in advance for any assistance.