Canonical set of books covering Bachelors and Masters in Economics?
Econ isn't as sequential as physics. The two core undergrad classes that everyone takes are Intermediate Micro and Intermediate Macro. Varian is the standard for Intermediate Micro.

Undergrads also take some sort of econometrics class, which can widely vary depending on the target audience (i.e., business majors vs double-majors). It's not uncommon for there to be an Econ degree geared towards double majoring.

After these courses, students generally pick about 5 electives. The classic books largely depend on the subjects at the undergrad levels. For Game Theory, Osborne is a good text as is Fudenberg and Tirole. The latter is a solid grad textbook as well. A good Auction Theory text is Krishna's. 

At the grad level, folks generally go for PhDs over Masters degrees. While Masters programs exist, they aren't as common as in math, physics, or CS. A good math for economists text is Simon and Blume. Mas-Collel is the classic for the grad micro sequence, which highlights game theory, IO, and general equilibrium. Jehl and Reyni is another good reference for micro, and it's a friendlier read.

Folks at the grad level also take sequences in macro and metrics. You may wish to check out Aris Spanos' text for metrics.