The question is about the actual physical setup and steps needed to take in order to experiment with the phenomena. I found a tutorial on jove.com, "How to Create and Use Binocular Rivalry", and it also has a dedicated explanatory article.
However, the experiment I want to make is tricky in the following sense.
A regular binocular rivalry experiment has two separate images set up, and normally the image features are controlled in a way that is suitable to exhibit a whatever the experimenters want.
In the case that I want to make, images are not separate, they are basically left and right parts of a single image that is usually viewed as a single image as well. With the experiment I will control left and right halves of that single image separately, but I do want to present halves to different eyes. The particular problem is that I want to calibrate the physical setup so that the physical boundary between images is not exactly visible. So it means I can't just split left and right - the border between the images in the eyes of the observer has to be as small as possible.
How can I present each half of a face, split vertically down the middle, independently to each eye (e.g., left half-left eye), without putting a visible physical boundary between the two image halves?
UPDATE: As advised in comments, I should say that the example stimulus is the two halves of one single face. The boundary between halves should not be seen to not potentially distract the observer or influence his perception elsewise.