canvass has 11 distinct synonyms spread across 9 of its 10 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
an inquiry into public opinion conducted by interviewing a random sample of people
a large piece of fabric (usually canvas fabric) by means of which wind is used to propel a sailing vessel
get the opinions (of people) by asking specific questions
solicit votes from potential voters in an electoral campaign
Synonyms, antonyms and the broader and narrower relations for canvass come from Princeton University’s WordNet. Full sources and licences.