What wires do you splice in a 3-way switch?
There are several ways to wire this circuit, but this is the one that will be least confusing to any future maintainers (which might even be you, two or three years from now).

I have put a &quot;C&quot; next to the common terminal on each switch.
Note that the white wires running to the remote 3-ways are marked with black paint or tape at both ends to indicate that they carry constant-hot and not neutral.