May one Kosher a meat vessel to use for dairy or vice versa?

May one Kosher a meat vessel to use for dairy or vice versa? Why not? Is there a difference between Libun and Hagallah? Is there a difference between Ashkenazi and Sephardic customs? Are there any cases of exception for Ashkenazim, such as if the vessels were left in storage and one no longer remembers their use, or one inherited vessels from their relative and would like to use it for the opposite food?