/invece di/ : in place of;
origin: in-vece, where /vece/ means 'substituting something or somebody'
examples:
-- potrei avere un gelato alla crema invece del caffe` ?
-- ho chiesto una tinta (paint) verde e invece questa e` rossa,
dovro` tornare al negozio.
-- (in the car) guarda bene la strada per favore, invece di parlare al telefonino!
/anzi/ : this introduces a second sentence which is not secondary to the primary, but has a contrast in meaning (with the first sentence), or emphasizes the meaning.
Examples:
-- domani non vado al lavoro, anzi andro` al mare per fare una bella gita in barca!
(contrast in meaning)
-- sto pensando di comprare una macchina nuova, anzi, - perche` no - anche una
casa piu` grande e piu` luminosa.
(original meaning "expanded")
-- vieni da me stasera ?, anzi, perche` non vieni a cena con la tua famiglia ?
E` da tanto che non ci incontriamo.
/piuttosto che/ : Eng. : rather than
may be used like /invece di/
A word of caution: since approx. 15 years ago, in Italy has been a wide spread of
the use of /piuttosto che/ with the simple meaning of /o, oppure/ (or); television is
the cuplrit, as speakers enjoy filling their mouth with the more sounding
/piuttosto che/ rather than the humble /o/. This is not good Italian usage, as
/piuttosto che/ has a contrast in its meaning, and /o, oppure/ usually join two similar
things and completely lack the "contrast" meaning.
Please don't follow this usage; it creates confusion into people who
want to follow the meaning of a conversation and are not satisfied
with just the sound of words.