Yes, there´s a reduction of the word "of" that somehow gets a v-sound to it. So, you hear "of a" with a sound similar to an "óva" phoneme (I am not using the phonetical formal way here, just one devised by me, as you did.)
Please read the Sentence Stress Part 6https://pronunciationcoach.wordpress.co ... ce-stress/
See the Example 2 to I should have got a cup of tea.
(“I should’ve gotta cupuv tea.”)
The same way it happens to "gotta" and "cupuv" (as per her explanation), it happens to your "ÂVA" (of a) and this is a sign that you are getting used to the sounds of English.
With time your ear will be so accostumed to it, in such way that you will discern it in spoken English, say, when listening an audio you can make it there.