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I have a few simple questions about Feynman Diagrams:

  1. Why, when $W^+$ or $W^-$ bosons are involved, sometimes the sign + or - is shown and sometimes not (example1, example2)?
  2. Why the arrow is usually not shown on bosonic lines?
  3. Sometimes I have the impression that for a single process, different equivalent Feynman diagrams exist. I give an example below. How can I decide in this case if the two diagrams have to be take into account or not? Is there a general rule?

The only difference is in the central top quark

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1. Why, when $W^+$ or $W^-$ bosons are involved, sometimes the sign + or - is shown and sometimes not?

The problem is that an X particle going from A to B is the same as an anti-X going from B to A, so there's ambiguity in whether any particular line ought to be labeled X or anti-X. The $W^+$ and $W^-$ are antiparticles of each other, so you could potentially write either sign on any $W$ line, and it's arguably better to leave it off since the charge can be inferred anyway from the interaction vertices.

2. Why the arrow is usually not shown on bosonic lines?

For fermions, there's a standard and well motivated division of the particles into matter and antimatter, and by convention the arrow points in "the direction the matter particle would go". If the arrow is future-directed then it's matter, while if it's past-directed then it's antimatter. (This is just a convention. Antimatter particles don't actually go backward in time.)

For bosons, while there's still a symmetry relating particles and antiparticles, there's no useful classification of the particles into pro and anti groups, so you can't use the same convention.

3. Sometimes I have the impression that for a single process, different equivalent Feynman diagrams exist.

The diagrams are the same. The arrow on the upper right line is future-directed, so it's a matter particle and is labeled as such. The arrow on the lower right line is past-directed, so it's an antimatter particle and is labeled as such. The arrow on the internal line is neither past nor future directed, so it can't be unambiguously labeled as top or anti-top. But it is unambiguously "either a top going up or an anti-top going down". The arrow and the $t$ label (with or without a bar) are enough to preclude any other interpretation.

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