Here is the solution:
var startDay = moment.utc("2013-06-02"); // Sunday (day before) in GMT
var startOffset = moment.utc(startDay).add("hours", 15).tz("Australia/Sydney").zone();// 15:00pm == -660 // 16:00pm == -600 // IN GMT
var startUTC = moment.utc(startDay).add('minutes', 1740).add("minutes", startOffset);
var endDay = moment(startDay).add('days' ,5); //moment.utc("2014-03-10"); // Friday in GMT
var endOffset = moment.utc(endDay).add("hours", 7).tz("America/New_York").zone();
var endUTC = moment.utc(endDay).add('minutes', 1020).add("minutes", endOffset);