What is the purpose of ϵ-transitions in PDA?
Yes, you could substitute the red transition for the black one below and have an equivalent PDA. With the black one, you allow the possibility that when reading $\mathtt{b}$s, you make a nondeterministic switch to the state where you expect to see a $\mathtt{c}$. If you do, it's as if you followed the red transition. In other words, either PDA will accept a string in $A$.

By the way, you could do a similar thing between the first and the second states of the upper branch.

The moral is that here are many roads to the top of the mountain, grasshopper.