@debdoris : As mentioned, the EPS format cannot maintain the transparency effects in the file. The .AI format does, of course, so it's a simple matter of opening the EPS in Illustrator and save it out as an .AI file instead (PDF will work too). Delete the checkerboard layer as it's just there to demonstrate the transparency. You can work with the file in Illustrator, or, you can now place it in an InDesign document. Keep in mind, the transparency effects only work if there's something behind it to interact with, e.g. you can't place it on a blank InDesign page. Also, keep in mind the colorspace of the file. It'll likely be in RGB as purchased (as many Transparency effects only work properly in RGB), so you would need to make sure your InDesign document is set to RGB Transparency space.
Regardless, it's a shame shutterstock doesn't simply provide an .AI file. But, even if they change their policy now, I doubt they have any interest in going back and resaving all the existing ones in .AI or .PDF... they don't have the working files, as any contributors only provide them with what they asked for, which is typically the ancient Illustrator 10 format.