I have seen this thread and I have a question about the picture describing the movement of electrons and holes.
Basic operation of a bipolar junction transistor
Here is my step by step way of thinking. B-E is forward biased and B-C is reverse-biased. Because B-E is forward biased, electrons move to the right from the emitter region to the collector region (because p is so narrow). Holes try to "meet" with the electrons at the left pn junction, \$i_{B1}\$.
Isn't \$i_{B2}\$ exactly doing what \$i_{B1}\$ is doing: combining its holes with the electrons at the pn junction?