The relationships among these clauses are mostly restatements. Paul's closing remarks are intensely pastoral and practical.  Having given his concluding exhortations in vv. 1-9, he ends by thanking the Philippians for their partnership in the gospel (a theme began in 1:6-8). Paul has written to a church that he deeply loves.

It is important to note the manner in which Paul expresses his gratitude. He thanks the Philippians by directing their minds and hearts to God. Paul seeks the fruit of their partnership, one for which they will be rewarded (v. 17). He is pointing them to the eternal paradigm (cf. 1:9-11; Hansen, PNTC, 321). This different paradigm continues as he also describes the gift he received from Epaphroditus (v. 18). This gift was a fragrant offering to God, acceptable and pleasing.

We should not simply skim through this without also considering how we thank others. Gratitude is a virtue of response to things that we do not deserve. Therefore, consummated gratitude must ultimately be to God Himself--Father, Son, Spirit. The culture of humility that is encouraged in 2:1-11 is one where gratitude abounds, specifically, gratitude that is primarily directed to God and His work by means of the people He puts around us. (See also, Carson, Basics for Believers, 120ff.)