So far, each inertial frame has its own meter bars at rest to measure distances, clocks at rest to measure durations, and elastic solid objects (threads, springs, etc.) to measure forces.
(Assumption) Every rigid or elastic solid object can be brought (to be at rest) into any inertial frame.
Backed by the principle of relativity, one can venture to say that:
(Principle) A rigid or elastic solid object has the same mechanical (incl. geometrical) properties in every inertial frame.
From this, it naturally follows that:
(Corollary) The units of length, time, and force can be synchronized between any two inertial frames K and K'.
To synchronize e.g. length, take a rod that is 1 meter long in K, bring it "up to speed" into K', and adjust the definition of 1 meter in K' accordingly. Similar applies to time and force. After that, the measuring tools of K and K' will be interchangeable in any mechanical experiment.
(Definition) Two inertial frames are of the same construction if and only if their units of measurement (length, time, and force) are synchronized.