RIVAS, Nicaragua—The steady breeze that spins the blades of towering white wind turbines here in southern Nicaragua is helping to shift this country further away from its dependence on Venezuelan oil—and closer to Washington’s vision for the region.

Since 2005, Venezuela’s socialist government has sent $70 billion of subsidized oil to Nicaragua and a string of other nations around the Caribbean, according to Barclays Investment Bank, through a program that secured political allies to help counter U.S. influence.

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