(b) Notwithstanding any provision of chapter 1 of this title, on or after July 1, 2013, and prior to July 1, 2014, both parties to a civil union entered into pursuant to this chapter may apply to the clerk of the peace in the county in which their civil union license was issued, for a marriage license, in accordance with procedures established by such clerk of the peace, to have their civil union legally converted to a marriage by operation of law without requirement of solemnization, provided that such civil union has not been previously dissolved or annulled and is not subject to a pending proceeding for dissolution, annulment or legal separation. Upon application for a marriage license in accordance with such procedures, such parties shall be issued a certificate of marriage and the civil union of such parties shall be converted to a marriage by operation of law. For all purposes of the laws of this State, the effective date of such marriage shall be deemed to be the date of solemnization of such original civil union. Alternatively, on or after July 1, 2013, and prior to July 1, 2014, both parties to a civil union entered into pursuant to this chapter may apply to the clerk of the peace, in the county in which their civil union license was issued, for a marriage license pursuant to chapter 1 of this title and such parties may have such marriage solemnized, prior to July 1, 2014, pursuant to chapter 1 of this title, provided that such persons are otherwise eligible to marry under § 101 of this title, such civil union has not been previously dissolved or annulled, and such civil union is not subject to a pending proceeding for dissolution, annulment or legal separation. Upon the solemnization of such marriage, the civil union of such parties shall be converted at such time to a marriage by operation of law. For all purposes of the laws of this State, the effective date of such marriage shall be deemed to be the date of solemnization of such original civil union.