Definitions for edge up
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Princeton's WordNet
edge in, edge up(verb)
push one's way into (a space)
Wiktionary
edge up(Verb)
to increase up to a target bit by bit.
Citation
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"edge up." Definitions.net. STANDS4 LLC, 2013. Web. 20 Jun 2013. <http://www.definitions.net/definition/edge up>.

