As mentioned in the documentation, you can add your own link types. They can be named whatever you want.
From your question it sounds like you might be asking about Gantt chart dependancies/relationships between tasks:
Are these the relationships you mean by "fresh-fresh", etc?
If so, while you can create your own link types along these lines, JIRA doesn't have functionality to restrict user actions based on them.
For example, you could create a "Finish to Start" link type, and link two issues with it, but JIRA will not actually prevent one issue from "starting" until the other issue has finished.
Finally, if it is Gantt chart type functionality you want, have a look at add-ons like Gantt-Chart for JIRA which provide this. There are a number of others, so you should research which fits your needs.
I hope this answer helps. If not, please add a bit more information/details on what you are trying to achieve and I am sure someone will be able to help.
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