I understand that the point of the wye-delta transform is to have the equivalent resistance between every pair of nodes be the same in each form of the circuit.
However, when I see the derivation for the concept, they treat the equivalent resistance between two nodes in the circuit's wye form to be as if no current flows into the other node. My question is, why? If one looks at the attached picture, for example, the equivalent resistance between nodes 1 and 2 is R1 + R3. The resistors are treated as if they are in series. In the real circuit, however, R2 could have drawn current. My instinct is that that would affect the situation and make it differ from treating the circuit as if R2 didn't exist at all and that all the current from R1 flows to R3.
I think my question might come from a lack of understanding of equivalent resistance, as lame as that may be. I am used to thinking of Req in terms of maintaining voltage-current character in a circuit (as in, the same current flows into and out of the equivalent resistor as it did the original element, and the same voltage is across the element), so I don't understand the method of finding equivalent resistance between two points while ignoring the current going into the third resistor. I don't understand how voltage-current character is conserved in that case.
Thanks to anyone who can help me understand this better!
EDIT: The derivation I'm referring to is as follows:
http://i.imgur.com/gffFTzt.png (the editor is screwing up and not letting me post the image in here). Note they set the equivalent resistances equal for each configuration. This is intuitive, except when the calculate the equivalent resistance of each branch they do not consider current flowing through the other branch (as in, Rxy = R1 + R2 as if they were in series, except the two are not in series. I don't understand equivalent resistance in this context)