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No. There's no synchronisation like that between stacks.

Can I create such mechanism by polling the output?
I'm using python.

You could use a shell script or the automation api to keep asking for "stack output" till you get something and then run "pulumi up" after

I want to ask it while the deployment is running
do `pulumi up` to all and when I need the output do the poling.

Right you can do that using automation api. It's a bit of an odd program setup because it's going to just block "pulumi up" till the outputs resolve, but it's possible:
<https://www.pulumi.com/docs/reference/pkg/nodejs/pulumi/pulumi/automation/#Workspace-stackOutputs>

I thought of something like this:
```
while True:
      my_stack = pulumi.StackReference("my-stack")
      value = my_stack.get_output(key)
      if value:
         return value
      time.sleep(10)```

That will crash in a pulumi program because it will try to create two resources called "my-stack"

You need to use automation api to do this

I'm using automation and LocalWorkspace
I will need to refresh the stack each time I query the outputs right?`

`stackOutputs` will do a fetch each time you call it