Typically you'd use a CI tool like Jenkins to run the Maven build that publishes your War file into Nexus. Nexus would then be used by whatever tool you're using to push the War onto the target tomcat environment:
There are lots and lots of options.
Jenkins post build SSH script
Run a post-build SSH task from Jenkins that does something like this on the target tomcat server:
curl "http://myrepo/nexus/service/local/artifact/maven/redirect?r=releases&g=myorg&a=myapp&v=1.1&e=war"
-o /usr/local/share/tomcat7/webapps/myapp.war
service tomcat7 restart
Rundeck
My preference is to use Rundeck for deployments, because it has a Nexus plugin, providing convenient drop-down menus of available releases.
There is also a Rundeck plugin for Jenkins that can be used to orchestrate a CI process with Jenkins performing the build, hand-over to Rundeck for deployment, followed by a Jenkins call-back to run the integration tests.
Chef
I also use chef which can be used to automatically deploy software in a pull fashion.
The artifact cookbook has direct support for Nexus, whereas the application_java cookbook uses a more generic "pull from a URL" approach that also works well.
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The list goes on, so I hope this helps.
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