If you are comfortable writing a Stash plugin there are events for when a PR is created/updated, which you can listen too and then update your CI system.
Some links which may help:
Quite possibly someone has already written something for your CI. Which CI server are you using?
Bitbucket Pipelines helps me manage and automate a number of serverless deployments to AWS Lambda and this is how I do it. I'm building Node.js Lambda functions using node-lambda ...
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