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Synonyms for Run (same or very similar meaning)

WordNet sense 1 (a small stream):
rill, rivulet, runnel, streamlet

WordNet sense 2 (an unbroken series of events):
streak

WordNet sense 3 (a race between candidates for elective office):
campaign, political campaign

WordNet sense 4 (a race run on foot):
footrace

WordNet sense 5 (a row of unravelled stitches):
ladder, ravel

WordNet sense 6 (the pouring forth of a fluid):
discharge, outpouring, discharge

WordNet sense 7 (change or be different within limits):
range

WordNet sense 8 (have a particular form):
go

WordNet sense 9 (have a tendency or disposition to do or be something; be inclined):
incline, lean, tend, incline, be given

WordNet sense 10 (cause something to pass or lead somewhere):
lead, lead, lead

WordNet sense 11 (stretch out over a distance, space, time, or scope; run or extend between two points or beyond a certain point):
extend, pass

WordNet sense 12 (continue to exist):
endure, persist, prevail

WordNet sense 13 (carry out a process or program, as on a computer or a machine):
execute

WordNet sense 14 (direct or control; projects, businesses, etc.):
operate

WordNet sense 15 (extend or continue for a certain period of time):
run for

WordNet sense 16 (deal in illegally, such as arms or liquor):
black market

WordNet sense 17 (flee; take to one's heels; cut and run):
bunk, escape, lam, scarper, run away, fly the coop, head for the hills, hightail it, take to the woods, turn tail

WordNet sense 18 (move along, of liquids):
course, feed, flow

WordNet sense 19 (be diffused):
bleed

WordNet sense 20 (keep company):
consort, consort

WordNet sense 21 (travel a route regularly):
ply

WordNet sense 22 (include as the content; broadcast or publicize):
carry

WordNet sense 23 (cause to emit recorded sounds):
play

WordNet sense 24 (perform as expected when applied):
function, work

WordNet sense 25 (guide or pass over something):
draw, guide

WordNet sense 26 (pursue for food or sport (as of wild animals)):
hunt, hunt down, track down

WordNet sense 27 (compete in a race):
race

WordNet sense 28 (the act of testing something):
test, trial

WordNet sense 29 ((American football) a play in which a player attempts to carry the ball through or past the opposing team):
running, running game, running play

WordNet sense 30 (progress by being changed):
move

WordNet sense 31 (reduce or cause to be reduced from a solid to a liquid state, usually by heating):
melt

WordNet sense 32 (become undone):
unravel

WordNet sense 33 (a score in baseball made by a runner touching all four bases safely):
tally


From the ODE community, based on WordNetadd/edit