who takes over if the vice president resigns
A vice presidential vacancy continued until a new vice president took office at the start of the next term.
Twenty-fifth Amendment to the United States Constitution
a vice presidential vacancy continued until a new vice president took office at the start of the next term. 
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Twenty-fifth Amendment to the United States Constitution [SEP] Section 2: Vice presidential vacancy
Section 2 addresses the Constitution's failure to originally provide a mechanism for filling a vacancy in the office of vice president during the term in which the vacancy occurred. Before the Twenty-fifth Amendment a vice presidential vacancy continued until a new vice president took office at the start of the next term. The vice presidency had become vacant several times due to death, resignation, or succession to the presidency, and these vacancies had often lasted several years.