Which Year of Arrival on U.S. Citizenship Application?

[darkerhorse]

If an Italian immigrated to the U.S. in 1911, returned to Italy, and then immigrated again permanently in 1913, which year of arrival would be referenced on his application for U.S. citizenship?

[darkerhorse]

Also, how common is it for a repeat immigrant to be recorded on a ship manifest mas never having been in the U.S. before?

Is there a reason an immigrant would lie about that?

[darkerhorse]

Or is it more likely a recording error?