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Sterilizing (boiling in water) only needs to be done once before your period begins. Not between every step.
This video is made by a company called "Organi Cup" and recommends you to use their products like Organi Wipes and Organi Soaps for cleaning the cup.
But in order to minimize the use of disposables, you can use any BASIC bar soap for cleaning or even rinse it with just water before inserting it back again.