The IPA is an amazing construct, they have symbols for pretty much everything that might occur in speech in any language. They have some great symbols and at advanced level you may like to investigate some of the subtle differences in vowels that they identify. But they have symbols for things which to a singer are merely shadings of primary colour, and in other cases (notably singing oo) they have no symbnol at all. Personally I think you are better off just getting your ear practised and accurate so that you become a sonic artist.
Singing vowels are more consistent than speaking vowels. They do not alter by language or regional accent. Remember, speech got started because people made expressive sounds. It started with the natural sounds of the throat, but over millennia the vowels shifted and changed. We have to dig down under those layers of change to find the natural sounds of the human body.
As we go though this chapter you will get to know the symbols I have adopted for the sounds. Its just a shorthand, you are welcome to make up your own. I hope, though that the symbols I have chosen make some kind of logical sense, and are easy to associate with their sounds. I have made them somewhat different from normal letters so that we can tell right away that they are sound symbols.
Ù Ø α - i ê â - ö å