I am on L1 visa from 2010 November. My L1 VISA is getting expired on 30th Sep 2013. Same employer is filing for H1B COS for the coming H1B cycle which is starting in April 2013 which would be active only from Oct 1st 2013. If My H1B COS petition is approved, can I stay in US without leaving US as my L1 visa expries by 30th Sep 2013 and H1B COS will be effect only from Oct 1st 2013. Please let me know if this is OK and any suggestions to avoid any problems in future like filing through premium processing.