Edge detector - transistor only
I'm not totally clear on what you are asking about, but I think you want a edge to glitch converter?  I'll assume that you have a positive going edge and want to have this result in a positive pulse.  Two common answers are a one-shot or a flip-flop with a R-C delay from output to reset.  However, you want to use discrete analog parts for some reason.

How about a capacitor-coupled emitter follower with a resistor and capacitor in parallel to ground on the emitter?  Assuming new edges don't come along until the circuit has had time to reset, the rising edge goes thru the capacitor and makes a rising edge on the output (emitter).  A resistor from base to ground makes the input to the transistor go away quickly and reset for the next edge.  Meanwhile the length of the output pulse is governed by the R-C time constant of the output capacitor and resistor.