Can I use an undamaged US immigration visa from a passport with a very slightly water damaged cover page photo?

I realize that I should replace my passport in the case of a slightly water marked ID-page (the top left 1/5 of the picture has slight discoleration). I have just been issued my US immigration visa as a separate page in my passport. If I get a new passport, can I still use the immigration visa from my old passport? (The visa page is 100% intact with no water damage).