A realist's interpretation of spacetime is that all spacetime points have a concrete existence and that an individual's mental events/experiences occur "all-at-once." I take the point of view, however, that mental events/experiences occur one-after-another. I do not regard time flow as an illusion. I believe time really does flow for the individual.
As we know, an individual mind perceives a succession of concrete 3-dimensional slices out of the abstract 4-dimensional manifold. Let's say an individual, Ann, perceives a given 3-dimensional slice of spacetime at the moment "now." I will call this moment "A1." Ann perceives another 3-dimensional spacetime slice a little while later at the "now" A2. A2 and A1 are not the same "now." The now A2 occurs after the now A1 during the course of Ann's subjective time flow.
Similarly, let us say that another individual, Betty, perceives a 3-dimensional slice at a moment "now." I will call this moment "B1." Betty perceives another 3-dimensional spacetime slice a little while later at a "now" B2. B2 and B1 are not the same "now." The now B2 occurs after the now B1 during the course of Betty's subjective time flow.
As we know, the theory of relativity allows spacetime points to occur simultaneously or in sequence. Whether two given spacetime points (S1 and S2) are simultaneous or sequential depends on the reference frame from which the points are observed.
In the example I describe above, the points A1, A2, B1, and B2 are not spacetime points or slices.(1) They are "moments" (i.e., "nows") that arise within the context of the two subjective time flows. In the example, we say that A2 occurs after A1 because A2 occurs after A1 during the course of Ann's subjective time flow. Similarly, we say that B2 occurs after B1 because B2 occurs after B1 during the course of Betty's subjective time flow. We can see that Ann's subjective "nows" (A1 and A2) can be temporally coordinated with one another and that Betty's subjective "nows" (B1 and B2) can be temporally coordinated with one another. However, since there is no objective/universal flow of time, Ann's nows (A1 and A2) cannot be coordinated temporally with Betty's nows (B1 and B2). (2) (3)
1. "Now" and "spacetime slice" are not synonymous. The same subjective "now" can be associated with different spacetime slices.
2. In a relativistic universe, there can be no objective/universal flow of time. Time flow has to be subjective and mind-dependent. (Vesselin Petkov discusses this point in his online papers: http://alcor.concordia.ca/~vpetkov/absolute.html)
3. The two series of "nows" are unrelated to one another temporally. Ann's subjective nows do not occur "before," "after," or "simultaneously with" Betty's subjective nows.