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I no nothing about eps format or using Imagemagick in windows and can not test this.
convert origin.eps -transparent white transparent.eps
You can make eps files transparent in conversion to images by two steps.
First you need a extra line in the eps file so IM can correctly determine the delegate calls it can use, and secondally you need a -channels RGBA before reading in the eps.
See http://www.cit.gu.edu.au/~anthony/graph ... postscript
for how I modified a PS file and later read it in with transparent background.
EPS is handled exactly the same way as PS