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I it true that any connected oriented 3-manifold with nonempty boundary can be obtained as a ramified cover of 3-ball with a ramification at a link?

  • link = a 1-dimensional submanifold with possibly nonempty boundary.

If answer is "YES", can we choose in addition the restriction of the covering at the boundary?
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I it true that any connected 3-manifold with nonempty boundary can be obtained as a ramified cover of 3-ball with a ramification at a link?

  • link = a 1-dimensional submanifold with possibly nonempty boundary.

If answer is "YES", can we fix choose in addition the restriction of the covering at the boundary?
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