Bi-wire v's single with jumper leads.

I think biwiring works if you can filter the HF and LF before the speaker cables, or even before your power amp.

The ideal would be according to me:

LF-power amp- speaker cable-tweeter
pre amp <
HF-power amp- speaker cable-woofer

This being 1 channel, if you have 3 way or more then repeat for each.
I don't understand why some 3 way speakers have bi-wire option shouldn't they have a tri-wire set up.

Bi wiring will not always give you a better sound. It really depends on the speakers and it's cross over design.
If you really want to go the bi wiring route then you need to go what I call true bi wiring meaning 4 seperate runs to each speaker. The 2-4 design is a bit waste of time and might as well use single wired with jumpers instead.
Hope this helps.

Flashunlock "The 2-4 design is a bit waste of time and might as well use single wired with jumpers instead."

That couldn't be any further from the truth. There will of course be systems where conventional bi-wiring results in no audible improvement, but it's generally (in mid-fi & better systems) a very effective and impressive tweak.

To expand on what I explained earlier, 2-4 bi-wiring has the same effect as putting the crossover at the speaker terminals, rather than in the speaker, thus greatly reducing the distance traveled by the combined high & low frequencies.
Basic electronics will tell you that once any kind of filter exists in a circuit (eg a high-pass frequency audio filter as in a crossover), then the ENTIRE CIRCUIT is only capable of carrying what that filter allows.
As an analogy; if you put a 100 ohm resistor in line with 0.01 ohm/metre cable, the entire cable will have a resistance of about 100 ohms; the resistor dictates what that cable can carry.
Removing the jumpers and bi-wiring means the low-pass filter (for the woofer) acts on the entire LF cable right back to the speaker terminals, and same for the HF cable.

EMF interaction between speakers is aided by the fact that output of an amp is separated from the speakers by inductance of the cable. Typical wire has inductance in order of 0.3uH/ft - equivalent to 0.188 ohm at 5kHz (counting 10ft both ways). It is 43x less then speaker's impedance but it is only -16dB of power. (our hearing is logarithmic). In addition amplifier's output impedance is in the similar order at 5kHz (or even worse).

How do you figure the emf of the LF driver (essentially a source at that point) sees a Z of the cable and amp that is less than the Z of the HF circuit? It is not even close. HF circuits typically have a resistor in series with the driver ( 2 or 2.5 ohms usually), that series resistance plus the R and L of the HF coil swamps the Z of the cable and amp. Additionally, the frequencies supplied by the LF driver that will fall in the passband of the HF crossover are attenuated by the passive components in the crossover of the LF circuit, particularly if that crossover is higher than first order as part of that crossover will have a low Z path that shunts the higher frequencies.