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I do similar, but frame it in terms of dependencies.

The database can live without the web server, but the web server doesn't work without the database.

Therefore webserver ---> database.

Key thing in that these deployment / context / container diagrams don't have a temporal axis. If you want to represent a flow, then you want a diagram where time has directionality, like a sequence diagram.

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yup, A interacts with B with the interaction originating from A.
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related tangent (outside of diagrams) lt < and gt > symbols are often dangerously ambiguous; does

    A > B > C  
mean "A then B then C"? or "A is superior to B which is superior to C"?
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