GOA, India - US Defense Secretary Ash Carter began a three-day visit to India on Sunday, seeking to advance a relatively new defense relationship with a country Washington sees as a counterweight to the growing power of China.In a sign of the importance Carter places on improving defense ties with India, the visit is his second in less than a year, and it kicks off in Goa, the west coast home state of Defense Minister Manohar Parrikar.For India, closer US defense ties would bring greater access to American technology, and it too has been alarmed by China's naval forays in the Indian Ocean. But India has been historically wary of drawing too near to any one country."India's very reluctant to be seen as too close to the United States, but the Pentagon is very bullish on this relationship," said Shane Mason, a research associate at the Stimson Center in Washington.It is also a favored initiative of Carter, who established a special cell within the Pentagon last year to promote cooperation with India."There's no question about where the United States-India relationship is going," Carter said on Friday, at a talk at the Council on Foreign Relations in New York. "We can control and influence the pace, and I want to do that."The US military has made clear it would like to do more with India, especially in countering China's moves.