Balanced means that each of the two conductors has the same relationship to ground. Typically that means neither is grounded and they're physically configured, meaning twisted, so both conductors also have the same capacitance and inductance to ground.
It is not necessary to use transformers to connect balanced things among themselves unless the CMRR of the stage fed by the signal is not good enough.
The pairs of wires I used were not balanced in that one of each pair was the ground wire. Luckily, no noise was induced into these pairs.
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