APOSTILLE is the legalization provided by the Office of the Secretary of State of the State where the document/certificate is issued.
NOTE: The Apostille is not a stamp on the certificate. It is a legalization, i.e. a document stapled to the birth/marriage/death certificate by the Secretary of State
U.S. Birth/Marriage/Death records related to the "Italian side" must bear an APOSTILLE (according to Hague Convention of Dec. 5, 1961) of the Secretary of State of the State in which the document was issued, (except for the Certificate of Naturalization and/or similar documentation).