Oct 21 (Reuters) - Tesla Inc (TSLA.O) wants to shift to a less expensive battery for its electric vehicles but first needs to figure out how to overcome political tensions to get a Chinese partner to build the iron-based batteries near its U.S. factories. The world's two biggest economies have yet to resolve disputes over tariffs, intellectual property rights and Chinese incursions into Taiwan's air defense identification zone. And China's sweeping regulatory crackdown, aimed largely at the technology sector, could pose yet another hurdle. China adopted the technology early and makes 95% of the world's Lithium Iron Phosphate (LFP) batteries,...