How can I view stereoscopic image pairs without a stereoscope?

Stereoscopy relies on a single phenomenon… each eye can only see one of the two images.

The only economical solution I can think of, short of building your own box with lenses, would be to scan the image then display it on your phone using something like Google Cardboard.

There is software that creates a similar effect:- virtual reality.

A stereoscope will present each eye with a different image to give the illusion of 3D. This is exactly what VR does.

However, you would need to scan your images and show them to each eye in a VR headset.
Unless you can get them into an old Nintendo 3DS, which simulated 3D on a 2D platform.

One of the simplest methods of emulating stereo viewing also requires no special software to view or create: animated GIF. Most full-featured image editors can create animated GIF files from a set of images; some will automate the process more, but it's simple enough to do manually without undue effort.

This works both with conventional stereo pairs and with multi-image like the Nimslo camera (intended for lenticular stereo prints). The images are pasted into an animated GIF file in a manner that causes them to display for a short time (.2 to .5 seconds per frame works well) in an order that seems to "tilt" the image right to left and back again. The GIF is then set to loop continuously, and any software that can display GIF (which is virtually everything that can view images) will show the image in a way your brain will interpret as 3D.

This works on phones, tablets, desktop or laptop computers, and even smart TVs -- anything that can display a GIF.

Alternatively, for printed images, you may be able to train yourself to "free view". This is a method of viewing stereo pairs without a viewer. It requires fooling your visual system into decoupling focus from convergence, to let you focus close while letting your eyes become parallel, as if viewing a distant object.

There are a number of tricks for this -- the simplest is to hold the page with the image with something distant behind it. Look at the distant object, and move the page until the two images overlap (or ideally, fully fuse), then switch your gaze to the fused/overlapped images and let them come into focus without losing fusion. This is actually what a stereo viewer is doing, but the use of lenses makes it much easier.

Fancy, https://www.amazon.com/Forestry-Suppliers-Pocket-Stereoscope-4x/dp/B00KTN0E9U/

Less Fancy: https://www.amazon.com/Hand-Held-Lorgnette-Deluxe-Viewers/dp/B07PRMPWDM/

Cheap as dirt: https://www.amazon.com/Camera-Stereo-Slide-Stereoview-Stereoscope/dp/B0036AZ1C8/

The method I use to view stereoscopic images - where two prints are side by side, is by:

1. placing the image a foot or two away then.
2. place my hand vertically as a divider - thumb in front of my nose, all fingers up, between my eyes
3. looking at the picture - move closer / further (depends on dimensions) to permit each image to overlap... when they overlap it's 3D. I suppose a paper or envelope would work as well as a hand.

For example, after googling for "produced by tilting the specimen stage" ... I found some nucleosomes and tried it with this article, pdf pg. 10, (book pg. 304). https://cyberleninka.org/article/n/175504.pdf from my laptop screen at 75% zoom, then on an external 24" monitor also at 75% zoom... sat back some 50cm / 20" away, was clear and 3D.

There is a possible low-tech solution which I saw used in Edinburgh's Camera Obscura.

Simply print out the images side be side (no gap between them, identical sizes) and put a (mountain) fold down the middle. Put your nose against the fold. Voila! Each eye sees a different image. No crossing eyes or headaches involved.

In the display in the camera obscura, the images are presented on the corners of a pillar and people put their noses against the corner of the pillar. There may be some perspective fuzziness, but there has to be a cost for such a simple solution.