Naturalize (verb) - the act of investing an alien with the status of a national in a given state; it may be accomplished as the result of voluntary application, special legislative direction, marriage to a citizen, or parental action. 

Recognition - in this case, recognition is referring to descendants of Italian citizens who are eligible for and wish to have their Italian citizenship recognized and will therefore become Italian citizens.

Renounce (verb) - to give up, refuse, or resign usually by formal declaration, ones status of a national in a given state.