Why is collector current independent on collector base voltage in active region
I believe that you're reading books on analog electronics - these books are not aiming to provide you with an understanding of semiconductor devices. Take any book on semiconductor physics and you'll find the complete derivation there.

In short (the below applies to NPN BJT):

It is because Collector-to-Base junction is reverse biased in the active mode of operation. 

This reverse biased junction just "passes through" the carriers injected from Emitter into Base and then diffused through Base to Collector. The amount of these carriers is dependent upon BE voltage, and this whole amount is swept across reverse biased CB junction, regardless of CB voltage (as long as it is reverse biased). Therefore the current depends strongly on \$V_{BE}\$, but is independent of \$V_{CB}\$.

It is the depletion region charge which creates the electric field which "sweeps" the carriers from Base to Collector side of the junction.

Please note that there are second order effects ("weaker" effects) which contain \$V_{CB}\$ dependency (see for example Early effect).