how to simplify Inflation year-on-year option to Zero-coupon option

Belgrade 2004 paper basically proposes that inflation year-on-year volatilities (and hence yoy options) are basically the spread vols between the Zero-coupon vols from (t0 to T) minus the zero-coupon vols from (t0 to T-1).

Is it possible to express the payoff and hence a year-on-year option unto zero-coupon options? I am trying to map the yoy vega's of my options so that they can be netted off against the vega's of the zero-coupon options.