It's almost impossible to make a complete list of supplies for your quilt project from the Stitchery Crossover technique. Once the blocks are stitched and crossed over, you'll need all the usual supplies that you'd normally need to finish the quilt - sewing machine, thread, additional fabrics for the quilt top - including sashing, extra borders, backing, binding, and batting materials - plus standard quilting supplies needed to baste the sandwiched layers and quilt the project.
BUT, there are a few extra supplies that you may not think about under normal quilting circumstances that are needed or may, at least, come in handy for a Stitchery Crossover quilted project.
Plain white (or solid color fabric that matches your stitchery fabric). Third from the top in the photo on the left.
Since the Stitchery fabric has a looser weave then quilt-shop quality woven cotton, it's a good idea to plan a layer of plain fabric between the quilt top and the batting layer of your quilt project. Over time, this extra layer of cotton fabric will diminish the possibility for your batting to beard through the spaces in the stitchery fabric.
The plain white fabric doesn't have to be as large as the backing, but it's a good idea to make sure its slightly larger than the quilt center to accommodate the stitching fabric.
While I don't recommend making this extra fabric layer purchase before you have a good sense of the final project size, keep in mind that this optional extra layer will be discussed with the quilt construction once your blocks are ready to become a quilt
A trip to the office supply store may yield some handy gadgets for your stitchery crossover project like a fun clip board for your stitch chart - a plain clip board will work just fine, but a fun clip board is even better, and a calculator, if you don't already have one for your quilty calculations.
Fine graph paper can be downloaded HERE. This was created just for Stitchery Crossover scribbling. Print as many sheets as you need or want!