is there some possibility to work with an open database like mysql, mariadb or other and ASP.NET vNext?
Perhaps a beta driver or something like that?
For ASP.NET vNext you can choose to target the full .NET Framework or a slimmed down, bin-deployable, cross platform, Core framework.
If you target the full .NET Framework then you get all the data access options you had before. If you target the CoreCLR then you can use the new version of Entity Framework (EF7). Currently we have the following providers available on CoreCLR; SQL Server, SQLite, and an in memory provider for testing. Of course, more providers will become available as we work towards RTM.
In addition to EF7, there are also the corresponding provider specific SDKs that EF is building on top of, and these can be used in application code as well (e.g. there is an implementation of SqlClient that can be used to access a SQL Server database).
You can read more about our plans for EF7 here - http://blogs.msdn.com/b/adonet/archive/2014/05/19/ef7-new-platforms-new-data-stores.aspx.