keep one's nose to the grindstone vs peg away

keep one's nose to the grindstone and peg away both are verbs.

Word	Noun	Adjective	Verb	Adverb
keep one's nose to the grindstone	No	No	Yes	No
peg away	No	No	Yes	No

As verbs, keep one's nose to the grindstone and peg away are synonyms defined as:

keep one's nose to the grindstone and peg away: work doggedly or persistently

Other synonyms of keep one's nose to the grindstone include keep one's shoulder to the wheel, plug away, slog.

keep one's nose to the grindstone (verb)	peg away (verb)
work doggedly or persistently	work doggedly or persistently