In a LOCALIZE calculation, localized M.O.'s (LMO's) in double and triple bonds and on atoms with two or three lone pairs are split into one LMO that is mainly sigma and one or two LMO's that are mainly pi. For example, a triple bond would consist of a sigma LMO and two pi LMO's.
When either RABBIT or BANANA is present in a LOCALIZE calculation, these LMO's would be replaced with hybrid LMO's that have equal amounts of sigma character in each M.O. In the case of double and triple bonds, the resulting LMO's are commonly referred to as banana-bonds because of their shape, although they look more like éclairs than bananas. In the case of two lone pairs on an atom, e.g., oxygen in a water molecule, the resulting LMO's are commonly referred to as rabbit-ears because of their shape, although they look make like ear-muffs than rabbit-ears. Other LMO's that cannot be mixed without changing their localization properties, such as sigma LMO's in single bonds and LMO's that represent a lone pair on an atom that has only one lone pair, are not affected when RABBIT or BANANA is present.
All three sets of M.O.'s, canonical, localized, and localized with RABBIT or BANANA, are equivalent, in that the sets are related to each other by unitary transforms. Use whichever set best first the current needs.