* Small weekly storage build drives up prices early * Reuters injection estimates ranged from 59 bcf to 74 bcf * Stock deficit to yr-ago grows, 5-yr avg surplus shrinks (Adds inventory data) NEW YORK, July 1 (Reuters) - Front-month U.S. natural gas futures, up early ahead of weekly storage data, see-sawed Thursday morning after a government report showed a smaller-than-expected weekly inventory build. Front-month gas NGc1 was trading up about 2 cents in the $4.64 per million British thermal units area when the weekly storage data were released at 10:30 a.m. EDT (1430 GMT). Prices shot up 12.1 cents, or 2.6 percent, to $4.737 right after the report, then slowly backed off again to near flat at about $4.62 by about 10:50 a.m. The U.S. Energy Information Administration report showed total domestic gas inventories rose last week by 60 billion cubic feet to 2.684 trillion cubic feet, not far from last year's record highs at that time and a level not normally reached until after the third week of July. [ID:nPRWPI54] The build, below the Reuters poll estimate of 64 bcf, widened the storage deficit to last year by 13 bcf to 27 bcf, or 1 percent. The surplus to the five-year average dropped 22 bcf to 287 bcf, or 12 percent, but still offered a comfortable cushion for rebuilding stocks for next winter. "The injection for last week was at the bullish end of the range of expectations and well below the five-year average for the date, a clearly bullish report that will also warrant a downward revision to our storage forecast for the next few weeks," said Tim Evans, energy analyst at Citi Futures Perspective in New York. (Reporting by Joe Silha; Editing by Marguerita Choy)

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