I'm curious about the pronunciation difference of '있다'.

While studying Korean, I learned that the pronunciation of the word '있다' differs between written and spoken language. For example, in textbooks it is written as '나는 펜이 있다', but in actual pronunciation it sounds like '나는 펜이 있어' or '저는 펜이 있어요'. I wonder why this difference occurs. I find this pronunciation difference confusing as I learn Korean. Especially when there are differences between text and speech. I am curious about how Koreans actually speak in places like Gangnam or Hongdae. Are there any people who have had similar experiences? I would like to know more about these pronunciation differences. I would appreciate advice on how to use them in real life, and in what situations these differences occur.