The phenomenon is called "Vowel reduction". It should be described in any textbook for foreigners.

In Russian VR is especially strong. Only stressed vowels are pronounced clearly, non-stressed vowels are pronounced so cursory that in fact turn into different sounds. If you ask native speakers which sound exactly should be pronounced in each concrete situation you will often get contradictory answers.

In my opinion non-stressed vowels should be pronounced non-clearly, that is all. It is important to make your speech comprehensive. Overarticulation often hinders understanding.

Also this phenomenon makes correct stressing in Russian particularly important.